(1) "Find": read the question, analyze the question and its relationships, and find out the ____________ used to make the equation;
(2) "Set": use the letters (e.g., x) to represent the _______ of the problem;
(3) "set up": represent the relevant quantities in algebraic form using the letters, and list the equations according to __________;
(4) "solve": solve the equations
(5) "check": check that the values obtained are correct and consistent with the actual situation, and write the answer;
(6) "answer": answer the question asked in the question.
Growth rate problem: 1, Hengli commercial building in September sales of 2 million yuan, October sales fell by 20%, the commercial building from November to strengthen the management, improve the operation, so that sales rose steadily in December sales reached 1,936,000 yuan, the average growth rate of these two months.
2, some kind of computer virus spreads very fast, if a computer is infected, after two rounds of infection there will be 81 computers are infected. Please use the knowledge you have learned to analyze, each round of infection in the average computer will be infected how many computers? If the virus is not effectively controlled, will there be more than 700 infected computers after 3 rounds of infection?
3, Wang Hongmei students will be 1000 yuan of new year's money for the first time according to a year of regular savings deposited into the "Children's Bank", the maturity of the principal and interest out, and will be 500 yuan of which donated to the "Project Hope", and the remaining and all according to a year! Regular deposit, the deposit of the annual interest rate has been adjusted downward to the first deposit of the annual interest rate of 90%, so that after the maturity of the principal and interest ****530 yuan, the first deposit of the annual interest rate. (Assuming no interest tax)
4, Zhou Jiazhong students will be the first time 1,000 yuan of New Year's money according to a year of regular savings deposited in the "Children's Bank", the maturity of the principal and interest out, and will be donated to the "Project Hope" 500 yuan, the remaining and all of the regular savings by one year, the "Project Hope". The remaining and all according to a year of regular deposits, the deposit of the annual interest rate has been adjusted downward to the first deposit when the annual interest rate of 60%, so that after the maturity of the principal and interest ****530 yuan, the first deposit for the annual interest rate. (Interest tax is 20%, only need to make a formula)
5, the city government in order to solve the problem of the public difficult to see the doctor, decided to reduce the price of drugs. After two consecutive price reductions of a certain drug from 200 yuan per box down to 128 yuan, the average percentage of this drug each time the price reduction is
Commodity Pricing: 1, Yiqun Boutique to buy a number of commodities at a price of 21 yuan per piece of the goods can be priced on their own, if the price of each piece of merchandise for a yuan, it can be sold (350-10a) pieces, but the The Price Bureau limits the profit on each item to 20%. How many pieces does the store need to buy if it plans to make a profit of $400? How much should each item be priced?
2, Lida dealership for a factory to sell a construction material (here, the agency sales refers to the manufacturer first free of charge to provide sources of goods, to be sold and then settled, unsold by the manufacturer is responsible for the disposal). When the selling price per ton is 260 yuan, the monthly sales volume is 45 tons. The dealership in order to improve operating profits, ready to take a price reduction in the way of promotion. After market research, it is found that when the selling price per ton decreases by $10 per ton, the monthly sales volume will increase by 7.5 tons. Considering all factors, every ton of construction materials sold *** need to pay manufacturers and other costs 100 yuan. (1) When the selling price per ton is 240 yuan, calculate the monthly sales volume at this time; (2) in accordance with the principle of "small profits and high sales", ask how much the selling price per ton of material, the dealership's monthly profit of 9,000 yuan. (3) Jing said, "When the monthly profit is the largest, the monthly sales are also the largest." Do you think this is correct? Please give reasons.
3, the state in order to strengthen the macro-management of the production and marketing of cigarettes, the sale of cigarettes to implement the policy of levying a surtax. Now know a certain brand of cigarettes per strip of the market price of 70 yuan, no surtax, the annual production and sales of 1 million, if the state levies a surtax, each sale of 100 yuan tax x yuan (called the tax rate of x%), the annual production and sales will be reduced by 10x million. To make the annual surtax collected on this operation is 1.68 million yuan, and the production and sales of cigarettes to be macro-control, the annual production and sales of not more than 500,000, ask the tax rate should be determined as what?
4, spring travel agency to attract the public group to go to Tianshui Bay
scenic area tourism, launched a dialog in Figure 1, such as the charge
fee rates. A unit to organize staff to go to Tianshui Bay scenic area
tourism, **** paid to the Spring Travel Agency travel fee
with 27,000 yuan. How many employees of this unit **** went to Tianshuiwan Scenic Area on this trip?
5, a toy store purchasing staff for the first time with 100 yuan to purchase "Penguin" toys, quickly sold out. The second time to purchase found that the wholesale price rose 0.5 yuan, with 150 yuan, the number of toys purchased than the first 10 more. Two batches of toys are sold for 2.8 yuan. How many toys were purchased the second time?
6, a shopping mall test marketing a cost of 60 yuan / piece of T-shirt, the provisions of the test period unit price is not lower than the cost of the unit price, and the profit shall not be higher than 40%, after the test found that the sales volume (pieces) and the unit price of sales (yuan / piece) in line with the primary function, and when the time; when the time; (1) Write the range of values of the unit price of sales; (2) the analytic form of a primary function; (3) if the shopping mall obtained Profit of yuan, try to write the profit and the unit price of sales of the relationship between the formula, the unit price of sales is set at how much, the mall can get the maximum profit, the maximum profit is how much?
Area Problems: 1, a length and width of 40 centimeters and 250 centimeters of rectangular tin, to cut off four equal small squares at its corners, folded into a rectangular carton without a lid, so that its base area of 450 square centimeters. Then what is the height of the carton?
2, as shown in the figure of a farm to build a rectangular chicken farm, chicken farm on one side of the wall (wall length of 18m), the other three sides of the fence with wooden fence, wooden fence length of 35m. ① the area of the chicken farm can reach 150m2? Can the area of the chicken yard be 180 m2? If so, please give a design; if not, please give reasons. (3) If the length of the wall is m, and the other three sides are surrounded by a bamboo fence, what role does the length of the wall m play in the solution of the problem?
3. A piece of wire of length 20cm is cut into two sections and a square is made with the length of each section of wire as the perimeter. (1) To make the sum of the areas of the two squares equal to 17cm2, what is the length of the wire after it is cut into two pieces? (2) Is it possible for the sum of the areas of the two squares to equal 12 cm2? If so, find the lengths of the two pieces of wire; if not, give reasons.
Travel problem: 1, A, B two places 82km apart, A ride a bicycle from A to B, 9 minutes later, B ride a bicycle from B to A at a speed of 2km per hour faster than A, the two people in the distance from the B point of 40km to meet. What is the speed of A and B?
2, A, B, respectively, from the distance of 20 kilometers A, B two places at the same time with the same speed to the same direction, after the encounter, the two continue to move forward, B's speed is unchanged, A per hour than the original more than 1 km, the results of the A arrived at the B after B will take 30 minutes to reach the A, how many kilometers per hour to go.
3, A, B two cities between the railroad distance of 1600 kilometers, after technological transformation, the implementation of the train speed up, speed up than the speed before the speed increase of 20 kilometers / hour, the train from the city of A to the city of B travel time decreased by 4 hours, the railroad in the existing safety conditions of the safety of the travel speed shall not exceed 140 kilometers / hour. Please use your mathematical knowledge to show that the train can be speeded up again under the existing conditions of this railroad.
4, A, B two people were cycling from A, B two places in the direction of each other, A first 1 hour later, B only set off, and after 4 hours of two people on the way to meet in C, after the meeting of the two people according to the original direction to continue to move forward. B by C to reach A on the way for some reason stopped for 20 minutes, as a result of B by C to reach A than A by C to reach B also 40 minutes ahead of time, known as B than A more than 4 kilometers per hour, for A, B two people cycling speed.
Engineering problems: 1, a company needs to be completed within a month (31 days) of the new office building renovation project. If A, B two engineering team to do, 12 days can be completed; if A, B two teams alone, A team than B team less than 10 days to complete. (1) A, B two engineering team alone to complete the project the number of days required. (2) If A team construction, the company needs to pay a daily fee of 2000 yuan; if B team construction, the company needs to pay a daily fee of 1400 yuan. In the specified time: A. A team alone to complete the project out of the B team alone to complete the project; C. A, B team cooperation to complete the project. Which of the above three options cost the least?
2, moving a warehouse of goods, if empty alone, A needs 10 hours to complete, B needs 12 hours to complete, C needs 15 hours to complete, there are two warehouses A and B of the stock of goods phase, A in the A warehouse, B in the B warehouse at the same time began to move the goods, C began to help A handling, and then turned to help B halfway through the last two warehouses of the goods at the same time to move the completion of C to help the A and B of each how much time? How much time does C help A and B? (column formula)
3, a, b two people are running at a constant speed in the loop road, traveling in the same direction, every 2 minutes to meet; with the same direction, every 6 minutes to meet, known as a faster than b, ask a, b every minute, how many laps?
4, an oil depot tanks have a, b two oil injection tube, alone open a tube filled with oil tanks than alone open a tube filled with oil tanks less than 4 hours, the two tubes open at the same time 3 hours later, a tube due to malfunctions to stop the oil injection, b tube continue to inject oil 9 hours after the injection tanks, ask the a, b two tubes are open to fill the tanks alone, the number of hours each need?
Engineering problems: 1, a company needs to be completed within a month (31 days) of the new office building renovation project. If A, B two engineering team to do, 12 days can be completed; if A, B two teams to do alone, the A team than the B team less than 10 days to complete. (1) A, B two engineering team alone to complete the project the number of days required. (2) If you ask A engineering team construction, the company needs to pay 2000 yuan per day; if you ask B team construction, the company needs to pay 1400 yuan per day. In the specified time: A. A team alone to complete the project out of the B team alone to complete the project; C. A, B team cooperation to complete the project. Which of the above three options cost the least?
2, moving a warehouse of goods, if empty alone, A needs 10 hours to complete, B needs 12 hours to complete, C needs 15 hours to complete, there are two warehouses A and B of the stock of goods phase, A in the A warehouse, B in the B warehouse at the same time began to move the goods, C began to help A handling, and then turned to help B halfway through the last two warehouses of the goods at the same time to move the completion of C to help the A and B of each how much time? How much time does C help A and B? (column formula)
3, a, b two people are running at a constant speed in the loop road, traveling in the same direction, every 2 minutes to meet; with the same direction, every 6 minutes to meet, known as a faster than b, ask a, b every minute, how many laps?
4, an oil depot tanks have a, b two oil injection tube, alone open a tube filled with oil tanks than alone open a tube filled with oil tanks less than 4 hours, the two tubes open at the same time 3 hours later, a tube due to malfunctions to stop the oil injection, b tube continue to inject oil 9 hours after the injection tanks, ask the a, b two tubes alone open the tanks full of oil when how many hours each need?
Dynamic geometry: 1, known: shown in Figure 3-9-3, in △, . Point from the point along the edge to the point to move at a speed of 1cm/s, point from the point along the edge to the point to move at a speed of 2cm/s. (1) If the points start at the same time, after a few seconds, the area of △ is equal to 4cm2? (2) If the points start at the same time, after a few seconds, the length of △ is equal to 5cm? (3) In (1), can the area of △ be equal to 7cm2?
Miscellaneous questions: 1. In a chess game, each player plays exactly one game with the other player, and the winner of each game is credited with 2 points, and the loser is credited with 0 points. If the tie, two players each recorded 1 point, the collar Division there are four students in all the players in the statistics of the total number of points, respectively, 1979, 1980, 1984, 1985. verified, there is a student statistics are not wrong. Try to calculate how many players participated in this tournament ****.
2, mechanical processing requires oil lubrication to reduce friction, an enterprise processing a large mechanical equipment lubrication with oil amount of 90 kg, with the oil reuse rate of 60%, according to this calculation, the processing of a large-scale machinery and equipment, the actual oil consumption of 36 kg. In order to build a conservation-oriented society, reduce oil consumption, the enterprise's A, B two workshops are organized to reduce the actual amount of oil consumption for research. (1) A workshop through technological innovation, the processing of a large mechanical equipment lubricating oil consumption fell to 70 kg, with the reuse of oil is still 60%. A workshop technical innovation, processing a large mechanical equipment, the actual amount of oil consumption is how many kilograms? (2) workshop B through technical innovation, not only reduce the amount of lubricating oil, but also improve the utilization rate of oil, and found that on the basis of technological innovation, lubricating oil consumption decreased by 1 kg each, the amount of oil will increase the utilization rate of 1.6%. So that workshop B processing a large mechanical equipment, the actual oil consumption fell to 12 kg. Asked workshop B after technological innovation, processing a large mechanical equipment lubrication oil amount is how many kilograms? How much is the reuse rate of oil?
Dynamic geometry: 1, known: shown in Figure 3-9-3, in △, . Point from the point along the edge to the point to move at a speed of 1cm / s, point from the point along the edge to the point to move at a speed of 2cm / s. (1) If the point starts at the same time from the point to the point, then the point will move at a speed of 2cm / s. (1) If the points start at the same time, after a few seconds, the area of △ is equal to 4cm2? (2) If the points start at the same time, after a few seconds, the length of △ is equal to 5cm? (3) In (1), can the area of △ be equal to 7cm2?
Miscellaneous questions: 1. In a chess game, each player plays exactly one game with the other player, and the winner of each game is credited with 2 points, and the loser is credited with 0 points. If the tie, two players each recorded 1 point, the collar Division there are four students in all the players in the statistics of the total number of points, respectively, 1979, 1980, 1984, 1985. verified, there is a student statistics are not wrong. Try to calculate how many players participated in this tournament ****.
2, mechanical processing requires oil lubrication to reduce friction, an enterprise processing a large mechanical equipment lubrication with oil amount of 90 kg, with the oil reuse rate of 60%, according to this calculation, the processing of a large-scale machinery and equipment, the actual oil consumption of 36 kg. In order to build a conservation-oriented society, reduce oil consumption, the enterprise's A, B two workshops are organized to reduce the actual amount of oil consumption for research. (1) A workshop through technological innovation, the processing of a large mechanical equipment lubricating oil consumption fell to 70 kg, with the reuse of oil is still 60%. A workshop technical innovation, processing a large mechanical equipment, the actual amount of oil consumption is how many kilograms? (2) workshop B through technical innovation, not only reduce the amount of lubricating oil, but also improve the utilization rate of oil, and found that on the basis of technological innovation, lubricating oil consumption decreased by 1 kg each, the amount of oil will increase the utilization rate of 1.6%. So that workshop B processing a large mechanical equipment, the actual oil consumption fell to 12 kg. Asked workshop B after technological innovation, processing a large mechanical equipment lubrication oil amount is how many kilograms? What is the reuse rate of oil?
Second, basic questions, please do
1. Known rectangle perimeter of 20 centimeters, set the length of x centimeters, then the width is ( ).
A. 20-x B. 10-x C. 10-2x D. 20-2x
2. Students a, to every 10 people in a group, of which there are two groups of one less person each, then the students **** there are ( ) groups.
A. 10a-2 B. 10-2a C. 10-(2-a) D.(10+2)/a
Three, synthesis questions, please try
1. In extracurricular activities, Mr. Zhang found that students Most of them are 13 years old . So he asked his classmates, "I am 45 years old this year, a few years later your age is one-third of my age?"
2. Xiaoming's father saved 3,000 yuan for Xiaoming's education three years ago. When he withdraws it at maturity this year, he will get 3,243 yuan in principal and interest. Please help him calculate the annual interest rate on this kind of savings.
3. Zhao went to the store to buy exercise books, and asked his classmates when he came back: "The owner of the store told me that if I bought more, he would give me a 20% discount. So I bought 20 books and it turned out to be 1.60 yuan cheaper．" Can you make an equation?
Four, easy questions, please think about
1. construction workers pouring cement columns, to bend the rebar into squares. If the area of each square is 400 square centimeters, which type of rebar should be chosen from the list below?
Model A B C D
Length (cm) 90 70 82 95
Thinking point: solving the equation has two values, must be carried out to check whether the value obtained is correct and in line with the actual situation, because the length of the rebar is a positive number, so take x = 80, so should be selected to fold C type rebar.
2. Do you have mistakes in your work? Please record them and analyze the reasons for the mistakes .
6.3.2 Travel Problems
I. The focus of this lesson, please make sense of it
1. Basic relational formulas: _________________ __________________ ;
2. Basic types: Encounter Problems; Distance Problems; ____________ ;
3. Basic analysis method: draw a schematic diagram to analyze the problem, distinguish between speed and time, and find the equivalence (distance divided into parts).
4. Sailing problems of quantitative relationships:
(1) with the current (wind) sailing distance = against the current (wind) sailing distance
(2) with the current (wind) speed = _________________________
against the water (wind) speed = _________________________
2. Basic questions, please do them
1. A's speed is 4 kilometers per hour, so he travels ( ) kilometers in x hours.
2. B walks x kilometers in 3 hours, so his speed is ( ).
3. A walks 4 kilometers per hour and B walks 5 kilometers per hour, then A and B walk ( ) kilometers in one hour*** and ( ) kilometers in y hours***.
4, a section of the journey x kilometers, if the train travels at a speed of 49 km / h, then the train travels the full distance takes ( ) hours.
Three, comprehensive questions, please try
1. A, B distance of 180 kilometers, a person riding a bicycle from A every time to go 15 kilometers, another person riding a motorcycle from B, known as the motorcycle speed is the speed of the bike 3 times, if the two people set off at the same time, and traveled in the same direction, asked after how much time the two met?
2. a, b two places distance of 180 km, a person riding a bicycle from the first 15 km per hour, another person riding a motorcycle from the second, known as motorcycle speed is three times the speed of the bike, if the two people with the same direction, riding a bicycle in the first and the first departure 2 hours, ask the motorcycle after how much time to catch up with the bike?
3. A helicopter in A, B two cities between the flight, downwind flight takes 4 hours, upwind flight takes 5 hours . If the wind speed is known to be 30km/h, find the distance between the two cities A and B.
Four, easy questions, please think about
1. A, B two people are running at a constant speed in the 400-meter circular runway, two people in the same place at the same time to start the same direction and line, A speed of 100 m / min B speed is a speed of 3 / 2 times, ask (1) after how much time the two people met for the first time (2) the second encounter?
Thinking point: This question is about the same direction in the travel problem type. As can be seen from the question, A, B first encounter, B traveled one lap more than A; the second encounter between them the difference in distance for two laps of the journey. So after 8 minutes they meet for the first time and after 16 minutes they meet for the second time.
2. Do you have any mistakes in your homework? Please record them and analyze the reasons for your mistakes .
6.3.3 Blending Problems
I. The focus of this lesson, please make sense of it
Preliminary learning to equations to solve various types of application problems of blending problems; analyze the total amount is equal to the _________ basic method of a class of application problems and the key to it.
Second, basic questions, please do
1. someone with three days to make parts 330, known that the second day than the first day to do 3 more, the third day to do 2 times the second day 3 fewer, then he made the first day of how many parts?
Solution: If he makes x parts on the first day, then he makes __________ parts on the second day and ____________________ parts on the third day, according to the equation "A person makes 330 parts in three days"
: ______________________________________.
Solving this equation gives: ______________.
Answer: He made ________ parts on the first day.
2. First year A, B two classes have 48 and 52 students, now from outside the school transferred 12 people inserted into class A x people, the rest are inserted into class B, asked after the insertion of class A, there are students ＿＿＿＿＿＿, class B there are students ＿＿＿＿＿＿＿, if it is known that after the insertion of the number of students in class A, the number of students in class A, three times the number of students in class B, two times the number of students also more than four, listed in the equation is: ＿＿＿＿＿＿＿＿ ＿＿＿＿＿＿＿＿.
Three, comprehensive questions, please try
1. There are 23 people in A labor, 17 people in B labor, now transfer 20 people to support, so that the number of people working in A is the number of people working in B twice, how many people should be transferred to the A and B each?
2. In order to encourage water conservation, a place according to the following provisions of the monthly water bill: If each household does not exceed 20 tons of water per month, then each ton of water charged at 1.2 yuan; if each household uses more than 20 tons of water per month, then more than the portion of the charge of 2 yuan per ton. If a user's water bill for the month of May is an average of 1.5 yuan per ton, ask, the user should pay the water bill in May how many yuan?
3. A kind of candy unit price is 20 yuan per kilogram, B kind of candy unit price is 15 yuan per kilogram, if you want to prepare 200 kilograms of unit price of 18 yuan per kilogram of mixed sweets, and to make it and respectively, sales of two kinds of candy to maintain the same total income, ask how many kilograms of A, B two kinds of candy each?
Four, easy questions, please think
1. preparation of a concrete, cement, sand, gravel, water, the mass ratio is 1:3:10:4, to prepare this concrete 360 kilograms of various raw materials, respectively, how many kilograms needed?
Thinking points: the key to this problem is how to set the unknown, and then according to the part and equal to the overall equation to solve the problem. The cement is 20 kilograms.
2. Do you have mistakes in your homework? Please record them and analyze the reasons for your mistakes.
6.3.4 Engineering Problems
I. Key points of this lesson, please make sense of them
1. Basic relational equations in engineering problems:
Total work = work efficiency × work time
Sum of work in each part = Total work
II. Basic questions, please do
1. Doing a certain piece of work. A alone will take 8 hours to complete, and B alone will take 12 hours to complete, ask:
1) What fraction of the total workload will be completed when A does 1 hour? ＿＿＿＿＿ .
2) What fraction of the total workload is completed when B does it in 1 hour? ＿＿＿＿＿ .
3) What fraction of the total amount of work is done when A and B together do 1? ＿＿＿＿＿ .
4) What fraction of the total work is done when A does x? ＿＿＿＿＿ .
⑤ What fraction of the total work is done when A and B do x together? ＿＿＿＿＿ .
6 What fraction of the total work is done when A does 2 first? ＿＿＿＿＿ .
What fraction of the total work is done when B does 3? ＿＿＿＿＿ .
What fraction of the total work is done when A and B together do x? ＿＿＿＿＿ .
What fraction of the total amount of work is completed in three ****s?
The result completes the work, then the equation can be listed: ___ ________ ___
Three, synthesis questions, please try
1.A project, A alone to do 10 days to complete, B alone to do 15 days to complete, the two people work together for 4 days after the rest of the part of the B alone, how many days is needed to complete?
2. canteen storage of several tons of coal, the original daily burning 4 tons of coal, 15 tons used to improve the equipment, the amount of coal consumed to half of the original, the result is more than 10 days of burning, the original amount of coal.
3. A pool, a single open inlet pipe 3 hours to fill the pool, a single open outlet pipe 4 hours to drain the pool full of water. Now on the empty pool first open the inlet pipe for 2 hours, and then open the outlet pipe, so that the inlet pipe, the outlet pipe is open together, ask how many hours after the pool can be filled?
Four, easy questions, please think
1. a project, A alone to do 10 days to complete, B alone to do 15 days to complete, A alone to do 5 days, and then A, B cooperation to complete, **** to get 1,000 yuan, according to the workload of each person to complete the calculation of compensation, then A, B, the two should be how to allocate?
Thinking point of view: this question is to pay attention to the problem is the distribution of remuneration is based on their respective workload. So A and B each get 800 yuan, 200 yuan.
2. Do you have mistakes in your homework? Please record them and analyze the reasons for the mistakes .
6.3.5 Savings Problems
I.1. 1. The relationship between principal, interest rate, interest, and principal and interest:
(1) Interest = Principal x Interest Rate
(2) Principal and Interest = Principal + Interest
(3) After Tax Interest = Interest - Interest x Interest Tax Rate
2. By experiencing the "problem situation - the establishment of mathematical models - interpretation, application and extension" of the process, to understand and appreciate the role of mathematical modeling ideas in solving practical problems.
Two, basic questions
1. A product is sold at a 20% discount from its pricing at $14.80, then the original pricing is ________.
2. Shengchao deposited 1000 yuan of the New Year's money given by his father and mother in the bank at a fixed term of one year. The annual interest rate for a one-year term deposit is 1.98% and the interest tax rate is 20%. When the maturity withdrawal, the interest is _______
After tax interest ________,Xiaoming actually get the sum of principal and interest is __________.
3. Two kiosks, A and B, sell goods at the same price. A reduces the price by 10% a week later and raises it by 20% a week later, while B raises the price by 10% only two weeks later. _____ kiosks are selling at a lower price after two weeks.
4. A clothing vendor sells two sets of clothing at the same time, each set is sold for 168 yuan, at a cost of one set of profit of 20%, the other set of a loss of 20%, the sale of the vendor __________ (profit or loss)
Three, General
1. Xiaoming's father deposited the year before last year with a two-year fixed-term savings with an interest rate of 2.43% per annum, this year When it matures, the interest tax is deducted, and the interest tax rate is 20%, and the interest earned is exactly enough to buy a calculator worth 48.60 yuan for Xiaoming, so how many yuan did Xiaoming's father save the year before last?
2. Qingqing's mom bought a company's two-year bond for $4,500 the year before last, maturing this year, after deducting the interest tax,*** get the principal and interest of about $4,700, the interest tax rate is 20%, ask what is the annual interest rate of this bond? (Precise to 0.01%)
3. A store will be a model of color TV according to the original selling price increased by 40%, and then in the advertisement written on the "big reward, 20% discount", after customer complaints, law enforcement agencies according to the illegal income has been 10 times the fine of 2,700 yuan per unit of 2700 yuan, to find the original selling price of each unit of color TV?
Four, easy questions
1. a commodity buy unit price of 1500 yuan, if the sale of a commodity to obtain the gross profit is sold at 15% of the unit price, then the sale of this commodity unit price should be set at how many yuan? (Precise to 1 yuan)
Thinking points: by "profit = selling price - buying price" can be known that this commodity selling unit price should be set at 2000 yuan.
I. Careful selection (3 points per question, ***30 points)
1. If the sum of the squares of a number and half of it is equal to 5, then the number is ( )
A. 2 B. -2 C. 2 or -2 D. Neither of them is correct
2. One person suffered from influenza, after two rounds of infection *** there are 100 people who suffered from influenza, then the average number of people infected by one person in each round of infection is ( )
A. 8 B. 9 C. 10 D. 11
3. With 22cm of wire, folded into a rectangle with an area of 30cm2, the length of two sides of this rectangle is ( ).
(A) 5cm and 6cm (B) 6cm and 7cm (C) 4cm and 7cm (D) 4cm and 5cm
4. A polygon has 9 diagonals, then the number of sides of this polygon is ( ).
A. 6 B. 7 C. 8 D. 9
5. (2008 Jingzhou) A, B, C three supermarkets in order to promote a pricing are m yuan of goods, A supermarkets for two consecutive price cuts of 20%, B supermarkets a one-time price cut of 40%, C supermarkets for the first time to reduce the price of 30%, the second price cut of 10%, at this time, customers to buy this commodity the most cost-effective should go to the supermarket is ( ).
A. A B. B C. C D. B or C
6. From a square board sawed off 2m square wood strips, the remaining area is 48m2, then the original area of this board is ( )
A. 100m2 B. 64m2 C. 121m2 D. 144m2
7. A businessman cheaper than the price of goods by 8%. If the selling price remains unchanged, his profit (depending on the purchase price) can be increased from x to (x+10%), then x is ( ).
A. 12% B. 15% C. 30% D. 50%
8. New Year's Day, a group of people, New Year's Day to send each other a card, known as the whole group **** to send a card 132, then the group **** have ( )
A.11 (B.12 C.13 D.14
9. A company to the bank to borrow 20 million yuan, agreed to two years at maturity in a single payment. million yuan, agreed to two years at the expiration of a one-time repayment of the principal and interest, the interest is 12% of the principal, the company operates with this loan, two years at the expiration of the loan in addition to repaying the principal, interest, but also a profit of 40,000 yuan, if the operation of the period of the growth rate of the capital of the same percentage, then this percentage is ( ).
A. 22% B.10% C.20% D.15%
10. a commodity sold at 80% off the list price, can make a profit of 20%; if the list price of 70% off the list price, then (B ).
A. can make a profit of 10% B. can make a profit of 5% C. a loss of 10% D. a loss of 5%
II. patience to fill in (3 points per question, ***30),
1. the sum of the two numbers is 15, and the product is 56, then the two numbers are . ;
2. The perimeter of a right triangle is , and the length of the median on the hypotenuse is 1, then its area is . 1
3. (2008 Henan experimental area) in a 50cm long, 30cm wide landscape painting surrounded by a golden paper edge, made of a rectangular wall map, as shown in the figure, if you want to make the entire area of the planning land is 1800cm , set the width of the golden paper edge for cm, then meet the equation for
4. the number of people in the two groups product of 24, the number of people in group B The product of the two groups is 24, the number of people in group B is 2 more than the number of people in group A, then the number of people in group A is people, and the number of people in group B is people.
5. A television factory plans to spend two years to reduce the cost of a certain model of television sets by 36%, the average annual cost
6. a two-digit number, the first digit of the word than the tenth digit is larger than the number of 3, the first digit of the word is just equal to the square of the two-digit number, the two-digit number is __________
7. a unit to organize a Basketball League, every two teams are between the game 2 games, plans to arrange 90 games, set the invitation to x teams to participate in the game, then the equation can be .
8. As shown in the figure, in the Rt△ACB, ∠C = 90 °, AC = 8m, CB = 6m, point P, Q at the same time by the A, B two points were along the direction of the AC, BC to the point C moving at a constant speed, their speed are 1m/s, then after __________ seconds after the area of △PCQ for the area of the Rt△ACB half.
9. There is a bamboo pole, do not know how long he is, bar bamboo pole placed horizontally in front of a door, bamboo pole length than the width of the door more than 4 feet; to put the bamboo pole vertically placed in front of the door, bamboo pole length than the height of the door more than 2 feet; put the bamboo pole diagonally just and the door diagonally equal length, ask the bamboo pole length is __________
10. As shown in the figure, is the plan of the rectangular chicken farm diagram, one side of the wall (the wall length of) 18m), the other three sides with a bamboo fence, if the total length of the bamboo fence is 35m, the area enclosed is 150m2, then the length and width of this rectangular chicken yard are _______.
Third, answer the question (***40 points)
1. (6 points) a store in the "Dragon Boat Festival" came to the arrival of 2400 yuan to buy a number of boxes of rice dumplings, during the festival, each box at the price of 20% as the selling price, sold 50 boxes; after the festival, each box to less than the price of 5 yuan as the selling price, the remaining dumplings were sold. Sold the remaining dumplings, the whole process of buying and selling *** profit 350 yuan, ask the price of each box of dumplings.