Question 1. (Tai 'an Non-curriculum Reform in 2006) A beverage is made of two raw materials, A and B. The vitamin content of these two raw materials and the price of purchasing these two raw materials are known as follows:
A raw material b raw material
Vitamin content (unit/kg)
Price of raw materials (yuan/kg)
This drink must contain at least one unit of vitamin. If the mass of raw material A is, the inequality should be ().
A.B.
C.D.
A: A.
Question 2. (Henan Curriculum Reform in 2006) Two supermarkets, A and B, sell the same goods at the same price. In order to attract customers, they each offer different preferential schemes: after the accumulated goods purchased by supermarket A exceed RMB, the excess part is discounted at the original price; After the accumulated purchases in supermarket B exceed RMB, the excess will be discounted at the original price. Suppose the customer expects to buy RMB ().
(1) Please use the expression containing algebra to express the expenses paid by customers in two supermarkets respectively;
(2) Try to compare which supermarket is more conducive to customers' shopping? State your reasons.
Answer: Solution: (1) The cost of shopping in supermarket A is: yuan;
The cost of shopping in supermarket b is: yuan.
(2) When, it is solved.
When customers buy RMB, the cost of shopping in two supermarkets is the same;
When, Solution and Time.
That is, when customers spend more than RMB but less than RMB, it is more favorable to go to supermarket B;
When, solve,
That is, when customers spend more than RMB, it is more favorable to go to supermarket A.
Question 3. (Guangdong Curriculum Reform in 2006) Give some children a box of apples. If you give five apples to each child, there are still 12 apples left. If each child gets 8 apples, a child gets less than 8 apples. Find out the number of apples and children in this box.
Answer: Solution: If there are children, then apples are children.
According to the meaning of the question,
,
,
Because it is a positive integer, so take 5 or 6.
When,;
When.
A: There are five or six children and 37 or 42 apples.
Question 4. Liang Liang is going to buy an English repeater with the pocket money saved. Now he has 45 yuan, and plans to stay in 30 yuan every month from now on until he has at least 300 yuan. If he has at least one 300 yuan a month, the inequality that can be used to calculate the number of months needed is ().
A.B.
C.D.
Answer: b
Question 5. Xiaojie went to the school cafeteria to buy rice. He saw that there were as many people in line in front of the two windows (set as people) and stood at the back of the window queue. After two minutes, he found that four people bought food at the window every minute, six people bought food at the window every minute, and five people were added at the back of the window queue every minute.
(1) At this time, if Xiaojie continues to queue at the window, how long will it take him to reach the window (expressed by inclusion algebra)?
(2) At this time, if Xiaojie moves quickly from the window queue to the back of the window queue, and the time to reach the window is less than the time to continue queuing at the window, the value range will be obtained (regardless of other factors).
Answer: Solution: (1) What time does he continue to queue up at the window to reach the window?
(points)
(2) From the meaning of the question, you can get
,
Solve.
The value range of is.
Question 6. (Shiyan Curriculum Reform, Hubei Province, 2006) After market research, Kangzhi Dairy Co., Ltd. decided to implement "limited production and storage" for products A and B from next year, requiring them to increase production throughout the year. The total output value of this product (ten thousand yuan) conforms to: Given the relevant data shown in the table below, how should the company arrange the output of new products next year?
The output value of each product.
Jia Wanyuan
Ten thousand yuan
Answer: Solution: Suppose the company arranges to produce new product A, then the production of new product B depends on the meaning of the problem.
OK,
Solving this set of inequalities leads to,
According to the meaning of the question, you understand.
When,; When,; When.
Therefore, the company can arrange to produce new products A and B next year; Or produce a new product a,
Product b; Or produce new products a and B.
Question 7. (Weifang Curriculum Reform in 2006) A factory invested 200,000 yuan to purchase special equipment and molds for producing a new type of handicrafts. * * * To produce this kind of handicrafts, it is known that each handicraft needs to be put into 350 yuan, and each handicraft is sold to 550 yuan at the selling price. The sales profit of producing this handicraft = total sales revenue-total investment, so the following statement is wrong ().
A. if the output drops, the sales profit will be negative.
B. if the output is high, the sales profit is zero.
C. If the output, the sales profit is1000000 yuan.
D. if the output is high, the sales profit will increase with the increase of output.
Answer: c
Question 8. Weifang Curriculum Reform in 2006 According to Weifang Daily, Weifang Municipal Price Bureau issued the Notice on Adjusting the Water Supply Price in Weifang, stipulating that the current water price standard will be implemented from May this year 1 (see the table below).
Basic water price of water use category
(yuan/ton) sewage treatment fee (yuan/ton) water resource fee (yuan/ton) comprehensive water price.
(yuan/ton)
Water consumption base for residents' life and administration 1.80 0.90 0.50 3.20.
First gear outside the base 2.70 0.90 0.50 4. 10
Second gear outer base 3.70 0.90 0.50 5. 10
Industrial production water ...........
(1) As can be seen from the above table, the basic water price of the base water is 1.80 yuan/ton; The first basic water price outside the base [that is, the part exceeding 50% (inclusive) of the base] is charged RMB per cubic meter on the basis of the basic water price within the base; The basic water price outside the second base (that is, the part exceeding 50% of the base) is based on the basic water price within the base, and an additional yuan is charged per cubic meter;
(2) If the monthly water consumption of Li Mingjia's base is 6 tons, and his water consumption in May is 12 tons, what should Li Mingjia's water fee be in May (calculated according to the comprehensive water price)? If Li Ming's family plans that the water fee will not exceed that of 30 yuan in June, how many tons of water will Li Ming's family use at most in June? (accurate to 0.0 1)
Answer: (1) 0.9; 1.9;
(2) Solution: According to the meaning of the question, the water fee for 6 tons of Li Mingjia base in May was (yuan);
The water fee of 3 tons for the first gear outside the base is (yuan);
The 3-ton water fee for the second gear outside the base is (yuan).
Therefore, the water fee payable by Li Ming's family in May is (yuan).
Let Li Ming's family plan to use tons of water in June.
,
,
According to the meaning of the question,
Solve,
Li Ming's family used 8.63 tons of water in June.
Question 9. (Yantai non-curriculum reform in 2006) Xiaoming plays on the seesaw with his parents. The weight of three people is one kilogram, and his father is sitting at one end of the seesaw. Xiaoming, who weighs only half as much as his mother, and his mother are sitting at the other end of the seesaw. At this time, his father's end was still on the ground. Then Xiao Ming should weigh less than ().
kilogram
Answer: d
Question 10. (Maoming Curriculum Reform in 2006) In order to encourage residents to save water, the water fee in a certain place in our city is charged according to the following table:
The monthly water consumption of each household does not exceed 10 ton (including 10 ton) and the part that exceeds 10 ton.
Unit price of water fee 1.30 yuan/ton, 2.00 yuan/ton.
(1) If the water consumption of a household is tons and the water fee is RMB, the functional relationship between the water fee (RMB) and the water consumption (tons) is: (4 points).
(2) If Xiaohua's water fee is 17 yuan in April, ask him how many tons of water his family used in April? (3 points)
(3) It is known that every household in a certain community 100 paid a water fee of * * * 1682 yuan in May, and the water consumption of each household in that month did not exceed 15 ton (including 15 ton). What is the maximum number of households that may require water consumption of 65,438+00 tons in a month? (3 points)
Solution:
Answer: Solution: (1).
(2) Let the water consumption of Xiaohua in April be tons.
,
The water consumption of Xiaohua in April is 10 ton.
Judging from the meaning of the question,
,
(ton)
That is, the water consumption of Xiaohua in April is 12 tons.
(3) If the monthly water consumption does not exceed 10 ton, users who exceed 10 ton and do not exceed 15 ton are households.
Judging from the meaning of the question,
Simplify it,
.
So the maximum value of a positive integer is 6 1.
That is to say, there may be at most 6 1 household whose water consumption does not exceed 10 ton this month.
Question 1 1. (Liuzhou, Beihai Curriculum Reform in 2006) Organized by the Youth League Committee of a school, a knowledge contest was held around "Eight Honors and Eight Disgraces". Rules of the game: Each team must answer 27 questions, with 5 points for one correct answer, and 1 point for one wrong answer or no answer.
(1) By the end of question 18, the team of Class 03(3) scored 78 points. How many questions did the team in Class 03(3) answer correctly?
(2) According to the regulations of the competition, only when the score exceeds 100 (including 100), the team of Class 03 (3) can get 78 points at the end of the competition to answer 18 correctly, so how many questions must be answered correctly in the following competition to win the prize? Please briefly explain the reasons.
Answer: Solution: (1) Method 1: Set the team of Class 03(3) to answer the questions correctly.
According to the meaning of the question, you must:
That is, class 03(3) team answered correctly 16.
Method 2: Class 03(3) is assigned to answer the questions correctly and score.
According to the meaning of the question, you must:
When,
That is, class 03(3) team answered correctly 16.
(2) Method 1: If you answer the question correctly at least, you may win the prize.
According to the meaning of the question, you must:
solve
Is a positive integer.
Class 03(3) team must answer at least 6 questions correctly to win the prize.
Method 2: Answer the question correctly and get points to win the prize.
According to the meaning of the question, you must:
When,
Is a positive integer.
That is, the class 03(3) team must answer at least 6 questions correctly to win the prize.
Question 12. (Suzhou Curriculum Reform in 2006) China's "Labor Law" clearly stipulates the overtime pay of workers. During the "May Day" holiday, the day before is a legal holiday, and the employing unit shall pay overtime wages at a rate not lower than the daily or hourly wages of the workers themselves. The next day is a rest day, and the employer shall arrange for the workers to make up the rest first, rather than making other arrangements. Pay overtime pay according to the standard of not less than the daily wage or hourly wage of workers. Due to the need of work, Zhu Xiao worked overtime for three days on. Since the daily wage in Zhu Xiao is RMB, Zhu Xiao's overtime pay for three days during the May Day holiday should be no less than RMB.
Answer:
Question 13. (Suzhou Curriculum Reform in 2006) When driving, the driver found that it would take some time to step on the brakes in an emergency. This time is called reaction time, and then he will continue to drive a distance. We call the distance from the driver's discovery of an emergency to the stop of the car "braking distance" (pictured).
It is known that there is a relationship between the braking distance (unit:) and the vehicle speed (unit:), where is the driver's reaction time (unit:) and the braking coefficient. In order to test the change of braking distance of drivers after drinking alcohol, a certain institution conducted a "drunk" driving test on a certain type of car, known the braking coefficient of this type of car, and measured the reaction time of volunteers without drinking alcohol.
(1) If the volunteers don't drink, the speed is, and the braking distance of the car is _ _ _ _ _ _ _ _; (accurate)
(2) After drinking a bottle of beer for half an hour, the volunteers drove at the speed and measured the braking distance as. If volunteers drive at a new speed, how much will the braking distance increase compared with the situation without drinking? (accurate)
(3) If you drive this type of car in the future, the speed is to, and you should keep the distance from the preceding car to. If you find that the preceding car stops suddenly, how many seconds should your reaction time be less than to prevent "rear-end collision"? (accurate)
Answer: Solution: (1).
(2) Let the response time of volunteers after drinking be,
.
When.
.
Answer: the braking distance will be longer than when you don't drink.
(3) In order to prevent "rear-end collision", the braking distance must be less than,
,
Solve.
Answer: The reaction time should not exceed.
(Note: The braking distance between and is listed without scoring. )
Question 14. (Xiangtan Curriculum Reform in 2006) Xiaogang and Xiaoming went to a boutique stationery store and bought the same pen and the same exercise book. Answer the questions according to the following dialogue:
Xiao Gang: Aunt, I want to buy three pens and two exercise books. How much will it cost?
Shop assistant: Just 19 yuan.
Xiaoming: Aunt, how much does it cost to buy 1 pen and 3 exercise books?
Shop assistant: It only costs 1 1 yuan.
How much does (1) 1 pen and 1 exercise book cost?
(2) Xiaoming has money from 20 yuan and needs to buy 1 pen and some exercise books. How many exercise books can he buy at most?
Answer: Solution: (1) Suppose you need RMB to buy a pen and RMB to buy an exercise book.
According to the meaning of the question:
Get a solution
(2) Set the purchased exercise book as one.
rule
Because it is a non-negative integer, the maximum value of is.
Answer: (1) You need 5 yuan to buy 1 pen and 2 yuan to buy 1 exercise book. (2) Xiao Ming can buy at most 7 exercise books.
Question 15. (Guigang Curriculum Reform in 2006) A junior high school in our city held a knowledge contest of "Eight Honors and Eight Disgraces", with 50 answers. Rules for answering questions in time: 1 Deduct 3 points for answering questions, 1 Deduct 0 points for answering questions incorrectly, and deduct 0 points for not answering questions in time.
Answer: Solution: Ask Xiaojun to answer the question correctly. According to the meaning of the question:
Solution:
Is a positive integer.
The smallest positive integer of is 18.
A: Xiaojun must answer at least 18 correctly.
Question 16. (Guiyang Curriculum Reform in 2006) A car rental company wants to buy * * * cars and vans. Among them, at least one car should be purchased, each car 10000 yuan, each van 10000 yuan, and the company's investment should not exceed 10000 yuan.
(1) What are the purchasing schemes that meet the requirements of the company? Please explain the reason. (8 points)
(2) If the daily rent of each car is RMB, the daily rent of each van is RMB. Assuming that the newly bought car can be rented out every day, which of the above purchase schemes should be chosen to make the daily rental income of this car not less than RMB? (4 points)
Answer: (1) If you want to buy a car, then you want to buy a van.
.
Solution:.
Once again, and then ...
So there are three purchasing schemes: scheme 1: buy a car and a van; Option 2: buy a car and a van; Option 3: buy a car and a van;
(2) The daily rent for Option 1 is:
The daily rent for option 2 is:
The daily rent for Option 3 is:
In order to ensure that the daily rent is not less than RMB, the third option should be selected.
Question 17. (Hezhou Curriculum Reform in 2006) At present, there are 24 garment workers in Fu Lin Garment Factory who make shirts and pants of a certain brand every day, and each person can make 3 shirts or 5 pants every day.
(1) If the factory requires the same number of shirts and pants to be made every day, how many people should be arranged to make shirts and pants?
(2) It is known that making a shirt can make a profit, 30 yuan, and making a pair of pants can make a profit 16 yuan. If the factory requires a daily profit of not less than 265,438+000 yuan, how many workers should be arranged to make shirts at least?
Answer: Solution: (1) Suppose a worker is to be arranged to make shirts.
.
Solve it and get it.
.
A: We should arrange 15 workers to make shirts and 9 workers to make pants.
(2) A worker should be arranged to make shirts.
.
Solve it and get it.
A: At least 18 workers should be arranged to make shirts.
Question 18. There are two ways for disc rental shops to rent discs: one is to rent discs with a membership card, the membership card is 10 yuan every month, and the disc is rented for 60 cents; The other is to rent discs sporadically, 1 yuan. If Xiao Qiang often comes to this store to rent a disc, it is more cost-effective to rent a disc with a membership card if he rents at least one disc every month.
Answer: 26
Question 19. (Shaoxing Curriculum Reform in 2006) The postal department stipulates that if the weight of letters is less than100g (including100g), every 20g shall be stamped with 0.8 yuan stamp, and if the weight is less than 20g, it shall be counted as 20g; If it exceeds 100g, poke 4 yuan first; If it exceeds 100g, it shall be stamped with 2 yuan every 100g; If it is less than 100g, it is counted as 100g.
(1) How much does it cost to send a letter weighing 35g?
(2) If you send a letter with a 6 yuan stamp, how much does it weigh?
(3) Nine students from Class 7 (1) took part in the environmental knowledge contest. If each answer sheet weighs 12g and each envelope weighs 4g, please design a plan to send these nine answers in two envelopes to minimize the total amount of stamps.
Answer: (1) 1.6 yuan.
2) grams
Stock weight (gram) Total amount (yuan)
1 8
2 7
3 6
4 5
(3)
Therefore, the nine answers are divided into 1, 8 or 3 or 6, with the smallest total amount, namely 4.8 yuan and 4.8 yuan.
Question 20. (Ziyang Curriculum Reform in 2006) A table tennis training hall is going to buy a pair of table tennis rackets of a certain brand, and each racket is equipped with a table tennis. It is understood that both supermarkets sell this brand of table tennis rackets and table tennis. The price of each racket is 20 yuan, and the price of each table tennis is 1 yuan. Now both supermarkets are promoting sales. All the goods in the supermarket are discounted by 10% (original price), and the supermarket buys 654338.
(1) If you only buy the required rackets and table tennis in one supermarket, is it more cost-effective to go to the supermarket or the supermarket?
(2) If necessary, please design the most economical purchase plan.
Answer: (1) According to the meaning of the question, the cost of going to the supermarket to buy a racket and a table tennis ball is yuan, and the cost of going to the supermarket to buy a racket and a table tennis ball is yuan.
By, solve;
By, solve;
Leave, leave.
At that time, it is more cost-effective to go to the supermarket to buy; When, go to two supermarkets to buy the same; At that time, it is more cost-effective to go to the supermarket.
(If it is not specified in the conclusion of the previous step, no penalty will be deducted)
(2) When buying a racket, you should have table tennis.
If you only buy it in the supermarket, the cost is (yuan);
If you only buy it in the supermarket, the cost is (yuan);
If you buy a racket in the supermarket and then buy an insufficient table tennis in the supermarket,
The cost is (yuan).
Obviously,
The most economical purchase plan is: buy a racket in the supermarket and get a table tennis ball, and then buy a table tennis ball at a 10% discount in the supermarket.
Question 2 1. (Guigang Non-curriculum Reform in 2006) A junior high school in our city held a knowledge contest of "Eight Honors and Eight Disgraces", with a total of ***50 answers. Rules for answering questions in time: 1 Deduct 3 points for answering questions, 1 Deduct 0 points for answering questions incorrectly, and deduct 0 points for not answering questions in time.
Answer: Solution: Ask Xiaojun to answer the question correctly. According to the meaning of the question:
Solution:
Is a positive integer.
The smallest positive integer of is
A: Xiaojun should at least answer the question correctly.
Question 22. (Shenzhen Curriculum Reform in 2006) Several students in Grade Three took a group photo as a souvenir. It is known that it costs 0.80 yuan to develop a negative and 0.35 yuan to develop a photo. On the premise that each student gets a photo and uses the negative film, the average share of money is less than that of 0.5 yuan, so the number of students taking a group photo is ().
A.b. At least 6 people C. At most 5 people D. At least 5 people
Answer: b
Question 23. The school plans to buy 40 pens and several notebooks (the number of notebooks exceeds the number of pens). Stationery stores A and B are priced at 10 yuan/pen, and the discount method for notebook 2 yuan/this A store is 10% off for pens and 20% off for notebooks; Shop B bought five pens for 1 notebook. There is no discount for pens, but 7.5% discount for notebooks. What series of notebooks are more cost-effective to buy in shop A?
Answer: Solution: It is more cost-effective to buy some notebooks to visit A. 。
Go to shop a to buy accounts payable;
Buy 40 pens in store B and get 8 notebooks.
Actual payables.
From the meaning of the question, get
.
.
.
.
Answer: It is more cost-effective to buy a notebook with a size of less than 280 (a notebook with a size of more than 40) and go to A store.