The eighth grade first volume mathematics chapter 5 a function unit examination questions.
First, multiple-choice questions (***4 small questions)
1. Master Zhang drives from place A to place B, and the distance between the two places is 500 kilometers. There were 25 liters of oil in the tank before the car started, and several liters were added on the way. Before and after refueling, the car drove at a constant speed of 100 km/h. As shown in the figure, the relationship between the remaining oil y (liter) in the fuel tank and the driving time t (hour) is known. The following statement is wrong ()
A the functional relationship between the remaining fuel quantity y (liter) in the fuel tank and the driving time t (hour) is y =-8t+25.
B. refuel 2 1 liter on the way.
C. the car can still run for 4 hours after refueling.
D. when the car arrives at point b, there are still 6 liters of oil in the tank.
2. In the morning, Xiaogang goes to school along the only road (straight road) leading to school. On the way, he found that he forgot to bring his lunch box, so he stopped to call home. After his mother received the phone call, he rushed to school immediately, and Xiaogang also came back. After they met, Xiaogang rushed to school and his mother went home. It took her mother 15 minutes to get home, and then Xiaogang went to school for 3 minutes.
① When talking on the phone, the distance between Xiaogang and his mother was1250m;
② After the phone call, Xiaogang arrived at school 23 minutes later;
③ After Xiaogang met his mother, the speed for her to go home was150m/min;
The distance between Xiaogang's home and school is 2550 meters. The correct number is ().
1。
3. Party A and Party B run 500 meters on a straight runway with the same starting point, the same finishing point and the same direction, and those who arrive at the finishing line first will rest in place. It is known that Party A will start for 2 seconds first. During the operation, the relationship between the distance y (m) between Party A and Party B and the departure time t (s) of Party B is as shown in the figure, and the following conclusions are drawn: ① a = 8; ②b = 92； ③c= 123。 The correct one is ().
A. 123B. Only 12C. Only 13D. Only 23.
4. A communication company provides two charging methods for mobile phones: mode 1, and the basic monthly fee is 20 yuan, and then the call time is charged at the price of 0. 1 yuan per minute; Method 2: The basic monthly fee is 20 yuan, and 80 minutes of talking time is given. The part exceeding 80 minutes will be charged at the price of 0. 15 yuan per minute.
Draw the following conclusions:
① The charging mode of 1 mode is described in the figure;
② If the monthly call time is less than 240 minutes, choose Scheme 2 to save money;
③ If the monthly communication fee is 50 yuan, mode 1 has more talk time than mode 2;
④ If the communication fee of mode 1 is more than that of mode 2 10 yuan, the talk time of mode 1 is more than that of mode 2 100 minutes.
The correct one is ()
A. only 12B. Only 34C. Only 123D. 1234C。
Second, answer the question.
A truck drove from A to B at a constant speed, and it took half an hour to unload after it arrived, and then returned at a constant speed. It is known that the return speed of the truck is 1.5 times the speed of the truck traveling from A to B, and the function image of the distance y (km) from A to B is as shown in the figure. What's the number of a? .
6. A county vigorously develops kiwifruit industry. It is estimated that 200 tons will be picked in A and 300 tons in B this year. If these kiwifruits are to be transported to two cold storages, it is known that warehouse A can store 240 tons and warehouse B can store 260 tons. The cost of transportation from A to A and B is 20 yuan and 25 yuan respectively, and the cost of transportation from B to A and B is 65438+ respectively.
(1) to obtain the functional relationships among yA, yB and x respectively;
(2) Try to discuss who has less freight between A and B;
(3) Considering the economic bearing capacity of place B, the freight of kiwifruit in place B does not exceed 4,830 yuan. In this case, how to transport the goods to minimize the sum of freight charges between the two places? Find this minimum value.
7.？ May day? During the Housing Fair, a real estate company in Duyun launched a real estate for sale: the first floor is a garage (temporarily not for external sales), and the second to third floors are all commercial houses (for external sales). The price scheme of commercial housing is as follows: the price of the eighth floor is 4,000 yuan/square meter, with an increase of one yuan per square meter from the eighth floor; On the other hand, every floor is lowered, and the price per square meter is reduced by B yuan. It is known that the price per square meter of the tenth floor is more than that of the sixth floor 100 yuan, and the price per square meter of the twentieth floor is more than that of the sixth floor by 400 yuan.
If the area of each commercial house is 100 square meter, the developer has formulated two purchase plans for the buyers:
Scheme 1: The buyer pays the down payment (30% of the total price of the commercial house) and then applies for installment payment (i.e. loan).
Option 2: The buyer pays off all the house payment in one lump sum, not only enjoying 9.9% discount, but also paying a certain amount less, which is the same as the five-year property management fee (it is known that the monthly property management fee is M yuan, and M is a positive integer).
(1) requests a and b;
(2) Write down the price per square meter Y (yuan/square meter) and the floor x(2? x？ 8, x is a positive integer);
(3) Wang Yang has made a down payment of125,000 yuan. If he buys a building with more than eight floors according to plan one, what is the highest floor he can buy?
(4) It was suggested that Li Qing use Option 2 to buy a commercial house on the 10th floor, but he thought that this option was not as cost-effective as directly enjoying a 10% discount on the house price. Do you think Li Qing's statement must be correct? Please clarify your point of view with specific data.
8. There are two warships A and B on mission in the South China Sea. They respectively travel from A and B to C in a straight line at the same time, and finally reach C (A, B and C are on the same straight line in turn). Suppose that after the two warships A and B travel x(h), the distances from B are y 1 (nautical mile) and y2 (nautical mile) respectively.
(1)① at 0? x？ During 5, the functional relationship between y2 and x is.
② At 0? x？ 0.5, the functional relationship between y 1 and x is
(2) The distance between A and C is in the sea.
(3) If the distance between two warships is less than 5 nautical miles, you can see each other, when 0.5? x？ At 3 o'clock, find the range of time x where two warships A and B can look at each other.
9. A shopping mall sells two brands of smart phones, A and B. The purchase price and selling price of these two brands are as follows:
Jiayi
Purchase price (RMB/unit) 4000 2500
Price (RMB/set) 4300-3000
The mall plans to buy two kinds of mobile phones at a cost of155,000 yuan. It is estimated that the gross profit after all the mobile phones are sold is * * * 2 100 yuan.
(Gross profit = (selling price-buying price)? Sales volume)
(1) How many mobile phones does the mall plan to purchase?
(2) Through market research, the shopping mall decided to reduce the purchase of type A mobile phones and increase the purchase of type B mobile phones on the basis of the original plan. It is known that the increase of B-type mobile phones is twice that of A-type mobile phones, and the total amount of funds used to purchase these two types of mobile phones does not exceed 6.5438+0.6 million yuan. How can shopping malls purchase goods to maximize the gross profit after all sales? And find the maximum gross profit.
10. a bus goes from a to b and a taxi goes from b to a. Two cars leave at the same time. Suppose the distance between the bus and A is y 1km, the distance between the taxi and A is y2 km, and the driving time of the two cars is x hours. The function images of y 1 and y2 about x are as follows:
(1) According to the image, directly write the functional image relationship between y 1 and y2 about X;
(2) If the distance between two cars is S kilometers, please write the functional relationship between S and X;
(3) There are two gas stations, A and B, which are 200 kilometers apart. If the bus enters the A gas station and the taxi just enters the B gas station, find the distance from the A gas station to the A place.
1 1. As shown in Figure ①, an empty cylindrical container with a bottom area of 30cm2 is horizontally placed with two solid cylinders. Geometry? At present, water is injected into the container at a constant speed until it is full. In the process of water injection, the relationship between water surface height h(cm) and water injection time t(s) is shown in Figure ②.
Please answer the following questions according to the information provided in the picture:
(1) The height of the cylindrical container is cm, and the water velocity of uniform water injection is cm3/s;
(2) What if? Geometry? The bottom area of the cylinder below is 15cm2 ~ 2. What? Geometry? Height and bottom area of the upper cylinder.
12. In progress? Beautiful Guangxi, clean countryside? During the activity, Township A plans to buy seedlings A and B 100. It is known that each seedling A is in 30 yuan and each seedling B is in 90 yuan.
(1) Suppose you buy X saplings of tree species A, and the total cost of buying two saplings of tree species A and B is Y yuan. Please write the functional relationship between y and x (the range of independent variable x is not required);
(2) If the total cost of purchasing two kinds of saplings, A and B, is no more than 7560 yuan, and the number of saplings of B is not less than 3 times that of seedlings of A, what are the options for purchasing saplings?
(3) From the perspective of saving money, which scheme do you think is more cost-effective?
13. A specialized farming household plans to buy two kinds of livestock, A and B. It is known that the unit price of the second kind of livestock is more than twice that of the first kind. In 200 yuan, it costs 5700 yuan to buy three kinds of livestock, 1 kind of livestock.
(1) What is the unit price of livestock A and B?
(2) If you buy 50 heads of the above two kinds of livestock, * * * will need 94,000 yuan. How many heads will you buy for each of these two kinds of livestock?
(3) Relevant data show that the survival rates of livestock A and B are 95% and 99% respectively. If the survival rate of these 50 livestock is not less than 97% and the total purchase cost is the lowest, how should I buy them?
14. The profit of a store selling 10 A and 20 B computers is 4,000 yuan, and the profit of selling 20 A and 10 B computers is 3,500 yuan.
(1) Find the sales profit of each type A computer and type B computer;
(2) The store plans to purchase two types of computers at one time *** 100, of which the purchase amount of type B computer is not more than twice that of type A computer. Suppose you buy X type A computers, and the total sales profit of these 100 computers is Y yuan.
① Find the functional relationship between y and x;
(2) How many A-type computers and B-type computers do stores buy to maximize the total sales profit?
(3) The manufacturer reduced the ex-factory price of Type A computer by m(0