(2) =___________。
2. Connect "
There are two strings of numbers arranged according to certain rules. Please fill in the blank figures according to the law.
( 1) ( );
(2) 15,20, 10,( ),5,30,( ),35。
4. There are three numbers A, B and C, and A and B are known; b，C； The average of C and A are 40, 46 and 43 respectively, so the average of A, B and C is _ _ _ _ _ _.
5. The following vertical Chinese characters, Shen, Ban, Ao and Yun, represent four different numbers respectively. I want to ask: Why do we need to establish a digital time formula for bidding for the Olympic Games? Shen = _ _ _ _; Do = _ _ _ _ _ Austria = _ _ _ _; Yun = _ _ _ _ _。
6. Class A has 48 students, including girls1/2; There are 45 students in Class B, of whom 1/3 are girls, so there are _ _ _ _ _ boys in Class Two.
7. To prepare 50 kg of 3% glucose, 1% and 6% glucose are _ _ _ _ _ _ _ kg respectively.
8. All five people belong to dragons. The product of their ages is 589,225, and the sum of the ages of these five people is _ _ _ _ _ _ _.
9. Processing a batch of parts. If the master processes it for 20 days first, the rest will be processed by the apprentice for 30 days. If the apprentice processes for 37 days first, the rest will be processed by the master 17 days. Now the master and the apprentice have been processing for a few days, and the rest will be processed by the apprentice for another 40 days. Q: The master and the apprentice cooperated for _ _ _ _ _ days.
10, use two cuboids with the same length of 3 cm, width of 2 cm and height of 1 cm to make a big cuboid, and its maximum surface area is _ _ _ _ _ square cm. (i.e. square centimeters)
Second, comprehensive questions: (6 points for each small question, ***30 points)
1. A shop bought 80 puppies and bear toys, but it has sold 1/5 puppies, 2/3 bears and 30. How many puppies and bears did you buy?
2. There is a book. If you read 35 pages on the first day, you will read 5 more pages every day than the day before. As a result, you only read 35 pages on the last day; It is the same book. If you read 45 pages on the first day, you will read 5 pages more than the day before, and only read 40 pages on the last day. Q: How many pages does this book have?
3. Cut a red cuboid (3×4×5) into cubes of 1× 1× 1. How many cubes have only one red face and no red face?
4. Beads with five colors of red, yellow, blue, white and purple are placed in five boxes numbered 1, 2, 3, 4 and 5 respectively. The guesses of A, B, C, D and E are as follows:
A: No.2 contains Callicarpa, and No.3 contains Callicarpa.
B: No.2 contains blue beads and No.4 contains red beads.
C: 1 contains red beads, and No.5 contains white beads.
D: No.3 contains blue beads and No.4 contains white beads.
E: No.2 contains yellow beads and No.5 contains Callicarpa.
As a result, everyone guessed one correctly, and only one person in each box guessed it correctly. What color are the beads that A, B, C, D and E guessed correctly?
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) to 7 (B) to 7 (C) to (d)
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 project of activity-based costing is ()
(A)4bca (B)4cab (C)acb (D)acb
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 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 quantity 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 ().
A A A = A .(B)(x)= x。
(C)3=9。 (D)3b 3c= 9bc 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 1 two years ago, so when they got together two years ago, the average age of everyone 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)X= (B)Y=-
(C)X & gt； (D)Y & gt； -
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
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 ||| and 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 filled in four small triangles is equal to zero, then the sum of the absolute values of these four numbers is equal to _ _.
40. Equation sum about x 3mx+7 = 0
2 x+3 n = 0 is the same solution equation, then
x-2y= 1999
The solution of the 4 1. system of equations {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. The known rule is _.
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 _.
1) Please write the sum of prime numbers not exceeding 30 in the nature book.
2) Please answer, 1 How many even natural numbers are there?
3) The thousands of four even natural numbers are 1. When it is divided by four different prime numbers, the remainder is also 1. Try to find all the natural numbers that meet these conditions. What is the biggest one?
A prime number 1 plus 6, 8, 12 and 14 is still a prime number, then this prime number is ().
2 Let A and B be natural numbers and satisfy 1 176a=b, then the minimum value of A is ().
-("Hope Cup" invitational test questions)
Of the n natural numbers of 3 1, 2,3 ┅ n, it is known that * * * has p prime numbers, q composite numbers, k odd numbers and m even numbers, then (q-m)+(p-k)= ().
4 It is known that P is a prime number and p +3 is also a prime number, so the value of p-48 is ().
5 Arbitrarily exchange the position of digits in 12345, and the number of prime numbers in five digits is ().
A 4 B 8 C 12 D 0
The single digit of the difference obtained by subtracting the product of all prime numbers not exceeding 60 from the product of all prime numbers not exceeding 100 is () —— (10th Hope Cup Invitational Tournament)
A 3 B 1 C 7 D 9
7 The greatest common divisor of all six digits (A, B and C are one of 10 numbers from 0 to 9, which can be the same and a≠0) and abcabc shape is () A100/b10/kloc-0.
7 when the integer n. >; When 1, the number that constitutes n +4 is ()
A prime number b composite number c composite number d even number complete square number
Is the sum of two prime numbers equal to a number? If yes, please give examples; If it does not exist, explain why.
middle (level)
1 If the prime numbers m and n satisfy 5m+7n= 129, the value of m+n is ().
2 n is not a prime number, and n can be decomposed into the product of two or more prime factors, none of which is greater than 10, and the minimum value of n is equal to (). -("Wuyang Cup" Competition)
3 if a, b and c are three different prime factors of 1998, and a < b < c, then (b+c) = ().
-("Wuyang Cup" Competition)
The result of supercomputer operation is that 2-1 is a prime number and 2+1 is a () number. (Fill in "Quality" or "Combination")
5 If the known natural numbers m and n are satisfied, then n= () (Shanghai Competition Question)
6 The robot dyes natural numbers from 1 from small to large according to the following rules; All natural numbers that can be expressed as the sum of two composite numbers are dyed red, and all natural numbers that do not meet the above requirements are dyed yellow. If the red number decreases from small to large, then the number 1992 is (). (Beijing "Spring Cup" Competition Title)
7 If three different prime numbers A, B and C are satisfied, then a+b+c= ()
elder
1 Write ten consecutive natural numbers, so that all are composite numbers. -(Shanghai competition topic)
2 Write the following numbers 2, 3, 4┅ 1994 on the blackboard. First, A erases one number, then B erases another number, and so on. If the last two numbers are reciprocal, A wins. If the last two numbers are not reciprocal, then B wins. Want to win, should choose A or B? Explain why. -(five-city league champion)
3 The product of three prime numbers A, B and C is equal to five times the sum of these three prime numbers, and it is evaluated.
Please take six different natural numbers at the same time, so that they satisfy at the same time:
Any two numbers in (1) 6 numbers are coprime;
(2) Take any two, three, four and five of the six numbers, and the sum of the six numbers is the composite number, and briefly describe the reasons why the selected numbers are qualified.
5 It is known that positive integers P and Q are prime numbers, and 7p+q and pq+ 1 1 are also prime numbers. Try to find the value of pq.