I. Multiple Choice Questions
1. (2008 Wuhan, Hubei) The solution set of an inequality is represented as (B) on the number axis.
A. B.
C. D.
2. (2008 Jiangsu Yancheng) real numbers on the number axis corresponding to the points shown in the figure, then , , the size of
relationship correctly (D)
A. B. C. D.
3. (2008 Yongzhou City) as shown in the figure, a, b, c, respectively, represent the apple, pear, peach The mass of the apple, pear and peach are shown in a, b and c, respectively. If the masses of the same kind of fruits are equal, the following relationship is correct (C)
A. a > c > b B. b > a > c C. a > b > c D. c > a > b
4. (2008 Yongzhou City) The following judgment is correct (）
A.................. < < ＜2 B. 2 < + ＜3
C. 1 < - <2 D. 1 < - <2 D. 4 < ? ．4 < ? <5
5. (2008 Taiwan) Solve the inequality x + 1? x + , and what is the range of its solution? ( )
(A) x? (B) x? (C) x? - (D) x? - .
6. (2008 Taiwan) A car passes through a tunnel 9 kilometers long at a rate of between 60 and 80 kilometers per hour. Which of the following could be the time taken by the car to pass through the tunnel? ( )
(A) 6 minutes (B) 8 minutes (C) 10 minutes (D) 12 minutes
7, (2008 Qiqihar) for the emergency resettlement of 100 earthquake victims, the need to set up at the same time to accommodate 6 people and 4 people of the two kinds of tents, then set up the program **** have ( )A
A. 8 B. 9 C. 16 D. 17
8 、(2008海南省) The solution set of the set of inequalities is ( ）
A. x > -1 B. x ≤ 1 C. x < -1 D. -1 < x ≤ 1
9 、(2008年陕西省) The solution set of the set of inequalities is correctly expressed on an axis ( ）Answer.
10 、(2008年江苏省无锡市), The solution set of the inequality is ( ）
A.
A. B. C. D.
11. (2008 Shuangbai County, Yunnan Province) The solution set of the set of inequalities is ( )
A. x > 2 B. x < 3
C. x > 2 or x < -3 D. 2 < x < 3
12. (2008 Huangshi, Hubei Province) If the set of inequalities has a solution, then the value of the (2008 Hubei Huangshi) If , then the magnitude relationship is ( )
A. B. C. D. Cannot be determined
14. (2008 Henan) The solution set of the inequality -x-5 ≤ 0 is represented correctly on the axis by ( )
14. (2008 Henan) The solution set of the inequality -x-5 ≤ 0 is represented correctly by ( )
14. (2008 Henan) The solution set of the inequality -x-5 ≤ 0 is represented correctly by ( )
15. The solution set of the inequality is ( )
15. (2008 Sichuan Luzhou) The solution set of the inequality is ( )
A. B. C. D.
16. (2008 Hunan Huaihua) The positive integer solutions to the inequality < are ( )
(A) 1 (B) 2 (C) 3 (D) 4
17. (2008 Chongqing) The solution set of the inequality -x-5 ≤ 0 is on the number line. (2008 Chongqing) The solution set of an inequality is correctly represented on the number line ( )
A B C D
18. (2008 Hubei Enshi) If a < b < 0, the following inequality is incorrect ( )
A. ab > 0 B. a + b < 0 C. < 1 D. a - b < 0
19. (2008 Hebei) The solution sets of the two inequalities in a certain set of inequalities are represented on an axis as shown in the figure.
This set of inequalities may be ( )
A. B. C. D.
20. (2008 Jiangxi) The solution set of the set of inequalities , , is ( )
A. B. C. D. No solution
(21) (2008 Nanchang, Jiangxi) The solution set of the set of inequalities , is ( )
A. B. C. D. No solution
22. The solution set of the set of inequalities can be expressed as ( )
A B C D
23. (2008 Linyi, Shandong) If the solution set of the set of inequalities is , the range of values of a is ( )
A. a>0 B. a=0 C. a>4 D. a=4 a = 4
24. (2008 Zhejiang Lishui) The solution to the set of inequalities is ( )
A. ＞1 B. ＜2 C. 1＜＜＜2 D. No solution
25. (2008 Sichuan Liangshanzhou) The solution set of the set of inequalities is correctly represented on the axis ( )
26. (2008 Ningde, Fujian) The solution set of the inequality is ( )
26. (2008 Ningde, Fujian) The solution set of the inequality is ( )
26.A. B. C. D.
27. (2008 Gansu Baiyin) the solution set of the inequality group expressed on the axis, the correct for the Figure 3 ( )
A. B. C. D.
28. (2008 Inner Mongolia, Chifeng) with the expression of the three different objects, is now placed on the balance to compare the two times, the situation is as shown in the figure, then these three objects according to the (2008 Zhejiang Lishui) the solution to the set of inequalities is ( )
A. ＞1 B. ＜2 C. 1 < < <2 D. No solution
30. (2008 Heilongjiang Qiqihar) for the emergency resettlement of 100 earthquake victims, it is necessary to build two kinds of tents that can accommodate 6 people and 4 people. 6 and 4 people of the two kinds of tents, then build program *** have ( )
A. 8 B. 9 C. 16 D. 17
31. (2008 Shandong Yantai) on the set of solutions to the inequality shown in the figure, the value of ( )
A, 0 B. 2 C, -2 D, -4
32. (2008 Taizhou, Zhejiang) The solution set of the set of inequalities can be expressed as ( )
33. (2008 Maoming, Guangdong) The solution set of the set of inequalities can be expressed as ( )
-2 -1 0 1 2 3 -2 -1 0 1 2 3
A B
-2 -1 0 1 2 3 -2 -1 0 1 2 3
A B
-2 -1 0 1 2 3 -2 -1 0 1 2 3
C D
34、(2008 Guangdong Zhanjiang) The solution set of the set of inequalities is ( )C
A. B. C. D. No solution
35、(2008 Yiwu) The solution set of the set of inequalities is represented on the axis as
II. Fill in the Blanks
1、(2008 Shandong Liaocheng) The set of integers known to exist with respect to the set of inequalities of There are 3 integer solutions to the set of inequalities ***, then the range of values is ．
2. (2008 Hubei Xiaogan) The solution set of the inequality set is .
3. (2008 Shandong Tai'an) The solution set of the set of inequalities is
4. (2008 Tai'an) The solution set of the set of inequalities is .
5. (2008 Shanghai) The solution set of the inequality is ．
6. (2008 Lianyungang City, Jiangsu Province) The solution set of the inequality set is ．
7. (2008 Hubei Xianning) straight line and straight line in the same plane right-angle coordinate system in the image shown in the figure, then the solution set of the inequality is ．
8, (2008 Qinghai Xining) "May 4th" Youth Day, the city of Beijing. Youth Day, the municipal Youth League Committee organized part of the secondary school members to go to the West Mountain tree planting. A school ninth grade (3) class branch received a number of saplings, if each person planted 4 trees, there are 37 trees left; if each person planted 6 trees, the last person to have a tree planted, but less than 3 trees, this batch of saplings **** there are trees.
9. (2008 Anhui Wuhu) function of the independent variable x in the range of values is ．
10, (2008 Hubei Tian'anmen) is known to the solution set of the set of inequalities is -1 < x < 2, then (m + n) 2008 = _______________.
Three, answer questions
1. (2008 Yongzhou City) (8 points) a logistics company, to transport 300 tons of materials to a certain place, the existing A, B two types of cars can be called, known as the A-type car can be loaded with 20 tons each, B-type car can be loaded with 15 tons each, in the case of each car is not overloaded under the conditions of the 300 tons of materials loaded and shipped, asked: in the five A-type car has been determined to call the premise at least need to call the B-type car, and then the B-type car can be loaded with 15 tons. How many B-type vehicles need to be called at least under the premise of the five A-type vehicles have been identified?
2, (2008 Guangdong) to solve the inequality , and the solution set of the inequality expressed on the axis.
3, (2008 Henan experimental area) solve the set of inequalities and represent the solution set on the drawn number line.
4, (2008 Shanxi Taiyuan) to solve the set of inequalities:
5, (2008 Hubei Xiangfan) "June 1" Children's Day eve, a fire department officers and men to understand that the earthquake-stricken areas of Wenchuan, a tent elementary school children like the Olympic Fuwa, on the special to buy some of them to give the elementary school of the Xio ah friends as a holiday gift. As a holiday gift. If each class is divided into 10 sets, then want 5 sets; if the front of each class is divided into 13 sets, then the last class although divided into Fuwa, but less than 4 sets. Q: How many classes in the elementary school? How many sets of Olympic Fuwa ****?
6. (2008 Zhejiang Huzhou) solve the set of inequalities:
7. (2008 Zhejiang Jinhua))Solve the inequality:5x- 3 < 1- 3x
8. (2008 Hubei Huanggang)Solve the set of inequalities
9. (2008 Hunan Zhuzhou)22. Tickets to the games of the 2008 Beijing Olympics are beginning to accept public booking . The following table for the Beijing Olympic Games official ticketing website announced several kinds of ball game ticket prices, a fan is ready to use 12,000 yuan to book 15 tickets for the ball games in the following table:
Match Program Ticket Price (yuan/game)
Men's Basketball 1,000
Soccer 800
Table Tennis 500
(1) if all the money used to booking tickets for men's basketball and table tennis, how many tickets for men's basketball and table tennis can this fan book?
(2) If the total number of tickets remains unchanged, the fan would like to reserve the same number of soccer and table tennis tickets as in the table above, and the cost of the soccer tickets does not exceed the cost of the men's basketball tickets, how many of each of the three types of tickets can be reserved?
10, (2008 Harbin, Heilongjiang) Rongchang company to transport the company's 100 tons of goods to a certain place for sale, after consultation with the Spring Morning Transportation Company, plans to rent a, B two types of cars **** 6, with the 6 cars will be transported all of the goods at once, of which each A-type car can be loaded with up to 16 tons of goods, each B-type car can be loaded with up to 18 tons of such goods. Known to rent a type A car and 2 type B car *** need to cost 2500 yuan; rent 2 type A car and 1 type B car *** need to cost 2450 yuan, and the same type of car rental costs per car the same.
(1) What is the cost of renting a Model A car and a Model B car?
(2) If Rongchang plans to rent a car for not more than 5000 yuan. Calculate how many car rental programs the company has? Please design it, and find the lowest rental cost.
11. (2008 Jiangsu Zhenjiang) Solve the set of inequalities
12. (2008 Hubei Xiantao, etc.) Solve the set of inequalities and put the solution set on the axis below.
13. (2008 Anhui Wuhu) Solve the set of inequalities
14. (2008 Ningbo) Solve the set of inequalities
15. (2008 Xuzhou) Solve the set of inequalities , and write down all its integer solutions.
16. (2008 Suzhou, Jiangsu Province) Solve the set of inequalities: and determine whether the set of inequalities is satisfied.
17. (2008 Shuangbai County, Yunnan Province) I county agricultural restructuring has been a great success, this year's fruit and a bumper harvest, a township organization 30 cars shipping A, B, C three kinds of fruits **** 64 tons of fruits to the field sales, the provisions of each car is only one kind of fruit, and must be loaded; and the shipment of each kind of fruit of the car is not less than 4; at the same time, the shipment of the B kind of fruit weighs Not more than the weight of the shipment of A, C two kinds of fruit and the sum of the weight.
(1) set with x cars shipment of A kind of fruit, with y cars shipment of B kind of fruit, according to the information provided in the following table, y and x to find a functional relationship between the y and x and write the range of values of the independent variable...?
Fruit species A B C
The volume of shipment per car (tons) 2.2 2.1 2
Profit per ton of fruit (hundred dollars) 6 8 5
(2) Let the profit of this export marketing activity be Q (ten thousand yuan), and find the equation of the relationship between Q and x. Please suggest a scheme for allocating the vehicles when the maximum profit is obtained.
18. (2008 Hunan Chenzhou) Solve the set of inequalities:
19. (2008 Jiangsu Nanjing) (6 points) Solve the set of inequalities. And express the solution set on the axis.
20. (2008 Shandong Jinan) Solve the set of inequalities , and represent the solution set on an axis.
21. (2008 Hubei Huangshi) a company has 40 pieces of type products, 60 pieces of type products, assigned to the subordinate A, B two stores to sell, of which 70 pieces to the A store, 30 pieces to the B store, and all can be sold out. The two stores to sell these two products per piece of profit (yuan) as follows:
Type profit
Type profit
Store A 200 170
Store B 160 150
(1) allocated to the store A type of product pieces, the company sold these 100 pieces of products for a total profit of (yuan), find the functional equation on the relationship, and to find the value range;
(2) The company has 40 pieces of type of products, 30 pieces of them to store A, and all can be sold. range;
(2) if the company requires that the total profit is not less than 17560 yuan, explain how many different distribution programs, and will be the design of the various programs;
(3) in order to promote the company decided to sell only the type of products in store A concessions, concessions of yuan per piece, but concessions of type of products after each profit is still higher than that of the type of products in store A per piece of profit. The type of products in store A, as well as the type of products in store B, the profit per piece of the same, asked the company and how to design the distribution plan to maximize the total profit?
22. (2008 Henan) a school eighth grade English speech contest, sent two teachers to the school near the supermarket to buy notebooks as prizes, after learning that the supermarket's A, B two notebooks prices are 12 yuan and 8 yuan, they are ready to buy these two notebooks **** 30.
(1) If they plan to use 300 yuan to buy prizes, how many copies of each of the two notebooks can they buy?
(2) Based on the prizes for the speech contest, the two teachers decided that the number of notebooks of type A to be purchased should be less than the number of notebooks of type B , but not less than the number of notebooks of type B , if they are set to buy n of the notebooks of type A, and it will cost w dollars to buy these two types of notebooks ****.
①Write the relation w (yuan) about n (books), and find the range of values of n;
②Please help them calculate, when they buy each of the two kinds of notebooks, spend the least, at this time, how much is spent on the yuan?
23. (2008 Hunan Changsha) solve the set of inequalities: , and its solution set on the axis.
24. (2008 Hunan Huaihua) 5.12 Sichuan earthquake, Huaihua City, immediately after the organization of medical staff rushed to the disaster area in Sichuan to participate in the rescue of the injured. To send 30 medical staff, carrying 20 pieces of luggage (drugs, equipment), rented A, B two types of cars **** 8, day and night to the disaster area. It is understood that each type of car can carry up to 4 people and 3 pieces of luggage, each type of car can carry up to 2 people and 8 pieces of luggage.
(1) If you want to rent a car of type A, please design all possible rental programs;
(2) If the cost of renting a car of type A and type B is 8,000 yuan and 6,000 yuan respectively, please choose the most cost-effective rental program.
25. (2008 Beijing) Solve the inequality , and express its solution set on the axis.
26. (2008 Anhui) Solve the set of inequalities , and express the solution set on the axis.
27. (2008 Hubei Ezhou) in order to better manage the water quality of Yanglan Lake, to protect the environment, the city sewage company decided to buy 10 sets of sewage treatment equipment. Existing two types of equipment, the price of each unit, the amount of sewage treatment per month as follows:
Type
Type
Price (million yuan / unit)
Treatment of sewage (tons / month) 240 200
After the investigation: to buy a type of equipment than the purchase of a type of equipment more than 20,000 yuan to buy 2 units of type of equipment than the purchase of 3 units of type of equipment less than 60,000 yuan. The company's business is to buy one type of equipment, which is 20,000 yuan more than buying one.
(1) Find the value.
(2) the budget: the municipal sewage treatment company to buy sewage treatment equipment, the capital does not exceed 1.05 million yuan, you think the company has which kinds of purchase program.
(3) in (2) asked the conditions, if the monthly requirements for the treatment of Yanglan Lake sewage is not less than 2040 tons, in order to save money, please design a most cost-effective purchase program for the sewage treatment company.
28. (2008 Hubei Xianning) "5?12" Wenchuan, Sichuan earthquake disaster has touched the hearts of the people of the country, a city A, B two vegetable bases learned in Sichuan C, D two settlements in need of vegetables, respectively, 240 tons and 260 tons of news, decided to transfer vegetables to support the disaster area. A vegetable base is known to have 200 tons of vegetables, B vegetable base has 300 tons of vegetables, now these vegetables are all transferred to C, D two victims of the settlement. From A to C, D, the cost of two places were 20 yuan per ton and 25 yuan, from B to C, D, the cost of two places were 15 yuan per ton and 18 yuan. Let x tons of vegetables be transported from B to C.
Fill in the table below and find the value of x when the freight charges for transferring vegetables from the two vegetable bases are equal;
C D Total
A 200 tons
B x tons 300 tons
Total 240 tons 260 tons 500 tons
Set the total freight charges for the two vegetable bases of A and B at $w. Write down the equation of the relationship between w and x,. And find the transportation plan that minimizes the total freight cost;
After repair, the road condition from B to C has been further improved to shorten the transportation time, and the freight cost has been reduced by yuan per ton (＞0), and the freight cost of the rest of the routes remains unchanged, try to discuss the transportation plan that minimizes the total freight cost.
29, (2008 Qinghai) Solve the set of inequalities and find the sum of all integer solutions.
30. (2008 Nanping, Fujian) Solve the set of inequalities:
31. (2008 Zigong, Sichuan) Solve the set of inequalities
32. (2008 Xiantao, Hubei, etc.) Solve the set of inequalities and represent the set of solutions on the axis below.
33. (2008? (Nanning, China) Solve the set of inequalities: , and represent its solution set on the axis.
34, (2008 Hei Long Jiang) a factory plans to produce two types of student tables and chairs for the earthquake zone 500 sets, to solve the learning problems of 1250 students, a set of type tables and chairs (a table and two chairs) need wood , a set of type tables and chairs (a table and three chairs) need wood , the factory's existing stock of wood .
(1) How many production options are there?
(2) now want to produce all the tables and chairs shipped to the earthquake area, known as each set of type tables and chairs of production costs 100 yuan, freight costs 2 yuan; each set of type tables and chairs of production costs 120 yuan, freight costs 4 yuan, the total cost of (yuan) and the production of the type of tables and chairs (sets) of the relationship between the formula and to determine the total cost of the least program and the least total cost. (Total cost Production cost Freight)
(3) Is there any wood left over from the program in (2)? If so, please write directly the maximum number of students that can be provided with tables and chairs by using the remaining wood to produce the above two models of tables and chairs again; if not, please explain the reasons.
Types of materials Food Medicine Daily necessities
The amount of each car (tons) 6 5 4
The required freight per ton (yuan / ton) 120 160 100
35, (2008 Guangdong Meizhou City, Guangdong Province) "a party in trouble, the eight parties to support". In the fight against the "5.12" Wenchuan earthquake disaster, a city organization 20 cars loaded with food, medicine, household goods three kinds of relief supplies **** 100 tons to the victims resettlement sites. According to the plan 20 cars to be loaded, each car can only be loaded with the same kind of relief supplies and must be filled. According to the information provided in the table on the right, to answer the following questions:
(1) set the number of vehicles for the shipment of food, the number of vehicles for the shipment of medicines. Find and the relationship between the formula;
(2) if the number of vehicles loaded with food is not less than 5, the number of vehicles loaded with drugs is not less than 4, then how many options for the arrangement of vehicles? And write each arrangement;
(3) Under the conditions of (2), if the total freight cost is required to be the least, which arrangement should be used? And find the minimum total freight cost.
36. (2008 Qingdao, Shandong Province) In August 2008, the Beijing Olympic Games sailing competition will be held in Qingdao International Sailing Center. There are two kinds of tickets to watch the sailing competition: A kind of ticket 600 yuan / piece, B kind of ticket 120 yuan / piece. A travel agency for a tour group to buy part of the tickets, in the purchase of tickets does not exceed 5,000 yuan in the case of the purchase of A, B two kinds of tickets **** 15, the number of A kind of tickets is not less than half of the number of B kind of tickets. If you set the purchase of A kind of tickets x, please answer the following questions:
(1) *** how many kinds of ticket program in line with the meaning of the question? Write the answer process;
(2) according to the calculation to determine: which ticket program is more economical?
37. (2008 Zunyi) (12 points) A supermarket sells two kinds of goods, A and B. Each piece of A costs 10 yuan and sells for 15 yuan; each piece of B costs 30 yuan and sells for 40 yuan.
(1) If the market at the same time a purchase of A, two kinds of goods **** 80 pieces, exactly 1600 yuan, how many pieces of A and B two kinds of goods can be purchased?
(2) the supermarket to make A, B two goods *** 80 yuan total profit (profit = selling price - purchase price) not less than 600 yuan, but not more than 610 yuan, please help the supermarket to design the corresponding purchase program.
38. (2008 Yiwu) Yiwu City is a "city on wheels", as of the end of 2007 the city's car ownership of 114,508 vehicles. Know
2005 the end of the city's automobile ownership of 72983. Please answer the following questions:
(1) The average annual growth rate of the city's automobile ownership from the end of 2005 to the end of 2007? (The result is accurate to 0.1%)
(2) In order to protect the urban environment, the city is required to have no more than 158,000 automobiles by the end of 2009, and it is estimated that from the end of 2007, the number of automobiles scrapped each year thereafter is 4% of the number of automobiles at the end of the previous year, so the maximum number of new automobiles each year is no more than how many automobiles? (Assuming that the number of new cars is the same each year, the result is accurate to a single digit)