1 A city collects the monthly water fee according to the following regulations: the water consumption does not exceed 6 tons, and the fee per ton is 1.2 yuan; If it exceeds 6 tons, the part that does not exceed will still be charged per ton 1.2 yuan, and the part that exceeds will be charged per ton of 2 yuan. If the average water fee of a user in May is per ton 1.4 yuan, how much should the user pay in May?

2. A person goes uphill at a speed of 3 km/h and downhill at a speed of 6 km/h, and the journey 12 km * * * It takes 3 hours and 20 minutes to try to find the distance between uphill and downhill.

3 (difficult). If two integers x and y make x2+xy+y2 divisible by 9, it is proved that x and y are divisible by 3.

4. Given 3x2-x= 1, find the value of 6x3+7x2-5x+2000.

5. A store sells 100 items a day, and each item can make a profit in 4 yuan. Now they increase profits by raising prices and reducing purchases. According to experience, every time the price of this commodity increases by 1 yuan, it will sell less 10 pieces every day. How much can we increase the price of each commodity to get the maximum profit? What is the maximum profit?

6. (Difficult) Finding the integer solution of equation | xy |-| 2x |+| y | = 4.

7. (Difficult) Wang Ping bought a three-year treasury bill with an annual interest rate of 7. 1 1% and a five-year treasury bill with an annual interest rate of 7.86% * * 35,000 yuan. If the principal and interest of three-year treasury bonds are deposited in two one-year time deposits, the total principal and interest of five-year treasury bonds will be 4776 1 yuan after five years. (It is known that the annual interest rate of one-year time deposit is 5.22%)

8. Find the integer solution of the indefinite equation 3x+4y+ 13z = 57.

9. (Difficult) Xiao Wang bought 40 fruits with 5 yuan money to entertain five friends. There are three kinds of fruits: apples, pears and apricots, each with 20 points, 8 points and 3 points respectively. Xiao Wang hopes that he and his five friends can get apples. Everyone gets a different number of apples. Can he achieve his wish?

10. Find the sum of the coefficients in the expansion of (8x3-6x2+4x-7)3(2x5-3)2.

1 1. A bucket of liquid pesticide, pour out 8 liters and fill it with water, then pour out 4 liters of mixed liquid and fill it with water. At this time, the pesticide concentration was 72%. Find the capacity of the barrel.

12. How many natural numbers x*** satisfy [- 1.77x]=-2x? Here [x] represents the largest integer not exceeding x, for example, [-5.6]=-6, [3] = 3.

13. (Difficult) Let p be a point in △abc. Find the distance range from p to △abc and the ratio to the perimeter of triangle.

14. Both Party A and Party B take the East and West Stations at the same time. When they meet, Party A travels 24 kilometers more than Party B, and it takes 9 hours for Party A to arrive at the East Station and 16 hours for Party B to arrive at the West Station. Find the distance between the two stops.

15. There are three numbers written on the blackboard. Erase one of them at will and rewrite it as the sum of the other two numbers minus 1, and so on, and finally get 19, 1997, 1999. Can the original three numbers be 2, 2 and 2?

17. It is known that the original price of commodity A is 0.5 times that of commodity B+65438. Due to market changes, the percentage of price increase of commodity B is twice that of commodity A.. After the price adjustment, the sum of the unit prices of commodities A and B is 2% higher than the sum of the original unit prices. Find the percentage of the price increase of commodity B.

18 (selected) In the acute triangle abc, all three internal angles are prime numbers. Find three internal angles of a triangle.

19. In the three-year plan of a factory, the annual output is increased by the same amount. If 1000 units are produced in the third year than originally planned, the annual increase percentage is the same, and the output in the third year is exactly half of the total output in the original three years. How many units will be produced each year according to the original plan?

20. 1 to 500 How many natural numbers appear in 1 or 5?

2 1 (selected). How many ways can you choose two different numbers from the 80 numbers 19, 20, 2 1, …, 98 to make their sum even?

22. A task with more than two items per day can be completed three days in advance, and with more than four items per day, it can be completed five days in advance. Try to find out the number of pieces of work and the time required to complete it as planned.

23. The two known serial numbers are 2, 5, 8, 1 1, 14, 17, …, 2+(200- 1) × 3,

5,9, 13, 17,2 1,25,…,5+(200- 1)×4,

They all have 200 projects. How many items in these two columns have the same number?

24 (difficult). Find the condition that x3-3px+2q is divisible by x2+2ax+a2.

25 (optional). If two triangles have the same corresponding angle, it is proved that the area ratio of these two triangles is equal to the ratio of the products of the two sides holding this angle.

26. It is known that the remainder of (x- 1)2 divided by the polynomial x4+ax3-3x2+bx+3 is x+ 1. Try to find out the values of a and B.

27. The length of a line segment is 1, 2, 3, …, 9 respectively. How many different methods can be used to select several lines so that they can form a square?

28. There are 10 straight lines on the (difficult) surface, four of which are parallel to each other. Q: How many parts can this 10 straight line divide the plane into at most?