1. An express train goes from A to B and a local train goes from B to A. Both trains start at the same time and travel at a constant speed. Let the travel time be x (hours) and the distance between two cars be y (kilometers). The dotted line in the figure shows the functional relationship between y and x from the start of two cars to the arrival of the express train at point B.

(1) According to the information in the figure, find the distance between the analytic function and A and B on the straight line where the line segment AB is located;

(2) It is known that when two cars meet, the express train travels 40 kilometers more than the local train. If the time required for the express train to reach the second place is t, find the value of t;

(3) If the express train returns to A immediately after arriving at B, and the local train stops after arriving at A, please draw a general picture of the function of Y on X in the process of returning from B to A (Tips: please draw it on the map corresponding to the answer sheet).

2. During Spring Festival travel rush, the passenger flow of a passenger station is increasing, and passengers often have to queue for a long time to buy tickets. According to the survey, about 400 people queue up to buy tickets every day, and new passengers are constantly entering the ticket office to queue up to buy tickets. At the time of ticket sales, four new ticket buyers are added every minute, and three tickets are sold every minute at each ticket window. On a certain day, the number of people waiting in line at the ticket office y (people) and the time of ticket sales x (minutes)

(1) Find the value of a 。

(2) At the 60th minute, the conductor listened to the number of passengers queuing to buy tickets.

(3) If all the passengers in the queue can buy tickets within half an hour after the ticket sales start, how many ticket sales windows should be opened at least at the same time so that passengers who arrive at the station later can buy them at any time?

3. There are three ports A, B and C on a straight line. Two ships, A and B, set out from ports A and B respectively at the same time, sailed to port C at a constant speed in a straight line, and finally arrived at port C. Suppose that the distance between the two ships A and B and port B is (km) after driving x(h), and the functional relationship with X is as shown in the figure.

(1) Fill in the blanks: the distance from port A to port C is km;

(2) Find the coordinates of point P in the diagram and explain the practical significance represented by the coordinates of this point;

(3) If two ships can see each other when the distance is less than 10 km, find the value range of x when two ships can see each other.

4. A vegetable company bought 140 tons of a green vegetable for processing and sales. The profit after sale is shown in the following table:

Sales method: sales after rough machining and sales after finishing.

Profit per ton (RMB) 10002000

It is known that the company's processing capacity is: finishing 5 tons or roughing 15 tons per day, but the two kinds of processing cannot be carried out at the same time. Due to seasonality and other conditions, the company must process and sell all these vegetables within a certain period of time.

(1) If 12 days processes 140 tons of vegetables, how many days should the company arrange for fine processing and rough processing?

(2) If finish machining is carried out first, then rough machining is carried out.

① Try to find the functional relationship between the sales profit of W yuan and the tonnage m of refined vegetables;

② If all 140 tons of vegetables are processed and sold within 10 days, what is the maximum profit from processing these vegetables? How to allocate processing time at this time?

5. Two trucks of a logistics company, A and B, travel from A and B in opposite directions at the same time and at the same speed. After passing through the distribution station C, Car A first arrives at C, and it takes 1 hour to deliver the goods at C, and then travels to B at the original speed. Car B goes straight from B to A, and the figure 16 shows the distance between the two workshops (km

(1) The distance between A and B is kilometers, and the A train will arrive at C in an hour.

(2) Find the value range of the function relationship between and between 2 hours after the departure of B train and the arrival of A train, and complete the function image in Figure 16;

(3) How long does the second train leave? The distance between the two trains is 150km.

6. Master Zhang drives litchi to a place where litchi is sold. Before the car started, there were 50 liters of oil in the tank. After driving for several hours, I added a few liters of oil at the gas station on the way. The relationship between the remaining fuel in the fuel tank (liter) and the driving time (hours) is shown in the figure.

Please answer the following questions according to the pictures:

(1) refuel after driving hours and refuel midway;

(2) Find the functional relationship between the remaining fuel in the fuel tank and the driving time before refueling;

(3) It is known that the car travels at a constant speed of 70km/h before and after refueling. If the gas station is 2 10km away from the destination, is there enough oil in the tank to reach the destination? Please explain the reason.

7. A school organized 340 teachers and students to carry out long-distance investigation activities, with 170 pieces of luggage. It is planned to rent two models 10 vehicles, A can carry up to 40 people and 0/6 pieces of luggage, and B can carry up to 30 people and 20 pieces of luggage.

(1) Please help the school design all feasible car rental schemes;

(2) If the rent of a car is 2000 yuan per car and the rent of b car is 1800 yuan, which feasible scheme can save the rent?

8. From June 20 10, 1 year, our province began to implement the policy of replacing old appliances with new ones. When consumers buy new home appliances limited by the policy, each new home appliance will receive certain subsidies. In order to ensure that the profits of enterprises are not lost, the government will provide subsidies. Three kinds of home appliance subsidies are as follows:

The subsidy amount is 10% of the sales price of new household appliances.

Note: The maximum amount of TV subsidy does not exceed 400 yuan/TV;

The maximum amount of subsidy for washing machines shall not exceed 250 yuan/Taiwan;

The maximum amount of refrigerator subsidy shall not exceed 300 yuan/Taiwan.

Therefore, the home appliance department of a shopping mall is going to purchase *** 100 TV sets, washing machines and refrigerators. The purchase price and sales price of these household appliances are as follows:

Purchase price (yuan/set) and selling price (yuan/set) of household appliances.

Television 3900 4300

Washing machine 1500 1800

Refrigerator 2000 2400

Assuming that the number of TV sets and washing machines purchased is X, the government needs to subsidize Y yuan for this 100 household appliances, and the profit obtained by the shopping mall is W yuan (profit = selling price-purchasing price).

(1) Please find the function expressions of y and x, w and x respectively;

(2) If the shopping mall decides to purchase not less than 30 sets of each household appliance, how many purchasing schemes are there? How should the shopping mall arrange the purchase if it wants to get the maximum profit? If all these 100 household appliances are sold, how much subsidy does the government need?

1.(20 10 Huzhou, Zhejiang) Answer (1) The resolution function of the straight line where the line segment AB is located is: y = kx+b,

Substitute (1.5,70) and (2,0) into:, and the solution is:

Therefore, the resolution function of the straight line where the line segment AB is located is y =- 140x+280. When x = 0,

Y = 280, then the distance between A and B is 280 kilometers.

(2) Let the speed of the express train be m km/h and the speed of the local train be n km/h. Judging from the meaning of the question:

So the speed of the express train is 80 kilometers per hour.

So ...

(3) As shown in the figure.

2.( 1) As can be seen from the image, so;

(2) If the analytical formula of BC is, substitute (40,320) and (104,0), so that when the ticket is sold to the 60th minute, 220 passengers are waiting in line at the ticket office.

(3) If six windows are opened at the same time, you can find out from the topic. Because it is an integer, at least six ticket sales windows should be opened at the same time.

3. Solution: (1)120;

(2) Obtained from point (3, 90).

When > 0.5, from points (0.5,0), (2,90),.

When,,,,.

At this time, the coordinate of point P is (1, 30).

The significance of this point coordinate is: after the two ships set out 1 h, ship A overtook ship B, and the distance between the two ships and port B was 30 km. ..

Another method for finding the coordinates of point p;

As can be seen from the figure, the speed of A is (km/h) and the speed of B is (km/h).

Then it takes (h) time for A to catch up with B, and the distance traveled by B at this time is (km).

So the coordinate of point P is (1, 30).

(3)① When ≤0.5, it is obtained from points (0,30) and (0.5,0).

According to the meaning of the question, ≤ 10. The solution is ≥

② When 0.5 < ≤ 1, according to the meaning of the question, ≤ 10.

Solution, ≥ So ≤≤ 1.

③> 1, according to the meaning of the question, ≤ 10.

Solution, ≤ So 1

To sum up, when ≤≤≤≤, both parties can meet.

4.(20 10 Neijiang, Sichuan) Answer: (1) Assuming that the finish machining is arranged for X days and the rough machining is arranged for Y days, the score is 1.

According to the meaning of the question: x+y = 12, 5x+ 15y = 140.3 points.

The solution is x = 4 and y = 8.

Answer: It takes 4 days for finishing and 8 days for rough machining. 4 points

(2) finishing m tons, rough machining (140m) tons, according to the meaning:

W = 2000m+1000 (140m)

= 1000m+ 140000。 6 points

② ∵ It is required to complete the processing of all vegetables within 10 days.

∴ M5+140-m15 ≤10, m ≤ 5.8.

∴0 0，

∴W increases with the increase of m,

When m = 5, wmax =1000× 5+140000 =145000. Nine points

∴ Finishing days are 5 5 =1,

Rough machining days are (140-5) ÷ 15 = 9.

Arrange 1 day finish machining and 9 days rough machining, and the maximum profit can be145,000 yuan. 10 point.

5.(20 10 Dalian, Liaoning) Answer

6.(20 10 Maoming, Guangdong) Answer: (1) 3,31.

(2) Assuming that the functional relationship between and is, according to the meaning of the question, we can get:

Solution: Therefore, the functional relationship between the remaining fuel in the fuel tank and the driving time before refueling is: (3) As can be seen from the figure, the oil consumption per hour (liters) of the car.

Therefore, the car should be equipped with oil (liter), because 45 liters >: 36 liters, so there is enough oil in the tank.

7.(20 10 Shantou, Guangdong) Answer: (1) If one car rents x cars, then one car rents (10-x). According to the meaning of the question, it is concluded that.

Get a solution

X is an integer.

∴x=4、5、6、7

∴ There are four feasible car rental schemes: ① 4 cars for A and 6 cars for B; (2) 5 cars a and 5 cars b; ③ There are 6 A cars and 4 B cars; (4) There are 7 cars A and 3 cars B 。

(2) If the total rental fee is Y yuan, then Y = 2000x+1800 (10-x),

That is y = 200x+ 18000.

∫k = 200 > 0，

∴y increases with the increase of x

∫x = 4、5、6、7

When ∴ x = 4, the minimum value of y is 18800 yuan, that is, renting 4 cars A and 6 cars B is the cheapest.

8(20 10 Benxi Liaoning)

answer