Basic questions:

First, multiple-choice questions:

1, which is a one-dimensional linear equation in the following categories is ()

A. B.

C. D.

2, the solution of the equation is ()

A. B. C. 1 D. - 1

3. If the solution of the equation about satisfies the equation, the value of is ().

A. 10 B. 8 C. D.

4, the following according to the nature of the equation is correct ()

A. by, get B. by, get

C. by, get D. by, get

5. When solving the equation, after removing the denominator, the correct result is ()

A. B.

C. C.

6. The price of TV sets has been reduced by10% for two consecutive times. After the price reduction, the price of each TV set is A yuan, so the original price of the TV set is ().

A. 0.8 1a yuan B. 1.2 1a yuan C. yuan D.

8. A store sells two pieces of clothes, each piece of 60 yuan, one of which earns 25% and the other loses 25%. Then after these two pieces of clothes are sold, the store is ().

A. Don't earn or lose B. Earn 8 yuan C. Lose 8 yuan D. Earn 8 yuan

9, the following equation, is a linear equation is ().

（A） （B） （C） （D）

10, the solution of the equation is ()

（A） （B） （C） （D）

1 1, given the equation, the following equation is not necessarily true ().

（A） （B）

（C） （D）

12, the solution of the equation is, it is equal to ()

（A） （B） （C） （D）

13, solve the equation, remove the denominator, and get ()

（A） （B）

（C） （D）

14, the following equation deformation, the correct is ().

(a) Equation, shift term, get

(b) Equation, without brackets, get

(c) Equation, the unknown coefficient is transformed into 1, and it is obtained.

(d) Equation formation

15, son 12 years old this year, father 39 years old this year, () father's age is four times that of his son.

(a) Three years later; (B)3 years ago; (c) Nine years later; (d) impossible.

16. The football used by chongqing lifan New Feeling Football Team for training is made of 32 pieces of black and white cowhide, in which the black leather can be regarded as a regular pentagon and the white leather as a regular hexagon. The ratio of the number of black and white leather pieces is 3:5, and the number of black and white leather pieces is required. If the number of black leather pieces is 0, the listed equation is correct ().

（A） （B）

（C） （D）

17. After the comprehensive building was built in Coral Middle School, there was a rectangular open space with a length of 5m more than width and a circumference of 50m. In order to beautify the environment, the school decided to plant it as turf. It is known that the lowest planting cost per square meter of turf is RMB, so planting turf requires at least ().

(a) yuan; (b) yuan; (c) yuan; (d) yuan.

One year, two years and three years.

2.25 2.43 2.70

18. The annual interest rate of bank education savings is shown in the following table on the right:

Xiaoming is now in the seventh grade. In July this year, his parents deposited 30,000 yuan in the bank for him to use in senior high school three years later. To maximize the income after three years, Xiaoming's parents should adopt ().

(a) Direct deposit for a period of three years;

(b) If the deposit period is 1 year, the interest sum will be automatically transferred to a 2-year period after 1 year;

(c) If one 1 year is deposited first, the interest and interest will be automatically transferred to two 1 year after 1 year;

(d) Deposit a 2-year deposit first, and automatically transfer the interest sum to a 1 year after 2 years.

2. Fill in the blanks:

1, then _ _ _ _ _ _.

2, known, then _ _ _ _ _ _ _.

3. If the solution of the equation about is 3, the value of is _ _ _ _ _ _ _ _ _ _ _.

4. If there is a three-digit number, its unit number is, the number on the tenth digit is, and the number on the hundredth digit is, then this three-digit number is expressed as _ _ _ _ _ _ _ _ _ _ _ _ _ _.

5. There are 96 students in Class A and Class B, and Class A has 2 more students than Class B, so Class B has _ _ _ _ _ _ _ _ _ _.

6. A number is 3 times larger than its half by 2. If a number is set as, the equation is _ _ _ _.

7. When _ _ _, the algebraic expression and the value of are opposite to each other.

8, in the formula, known, then _ _ _.

Day one two three four five six

1 2 3 4 5 6

7 8 9 10 1 1 12 13

14 15 16 17 18 19 20

2 1 22 23 24 25 26 27

28 29 30 3 1

9. As shown in the picture on the right, it is the calendar of February/2003/KLOC-0. Now, a rectangle is used to randomly frame 4 numbers in the calendar.

Please use an equation to express the relationship between _ _ _ _ _ _ _ _ _ _.

10, a long cylindrical test tube with an inner diameter of 3㎝ is filled with water. Now the water in the test tube is gradually dropped into a cylindrical glass with an inner diameter of 8㎝ and a height of 1.8㎝. When the glass is filled with water, the height of the water in the test tube drops by _ _ _ _ ㎝.

1 1 During the National Day, "New Century Department Store" had a seasonal discount. Jian Shuang bought a sportswear at a discount of 20% 16 yuan, so he actually spent _ _ _ yuan on this dress.

12, the total length of chengdu-chongqing railway is 504km. An express train departs from Chongqing at a speed of 90km/h, and after 1 h, another slow train departs from Chengdu at a speed of 48km/h, then the two trains meet _ _ hours after the slow train departs (excluding the stopping time at stations along the way).

13. When we were young, we heard the story of the race between the tortoise and the rabbit, and we all knew that the tortoise finally defeated the little white rabbit. If in the second race, the little white rabbit was ashamed and then brave, and when it was behind the tortoise 1 0 1 m/min, it would catch up at the speed of/kloc-0, but the tortoise still kept on.

14, the annual interest rate of one-year fixed deposit is 1.98%, and 20% of the interest must be deducted as interest tax and turned over to the state treasury. If Xiaoying deposits a one-year fixed deposit, the net interest after deducting interest tax is 158.4 yuan, then the RMB she has deposited is _ _ _ _ _.

15, 52 cars line up in two lines, each car is a meter long, the distance between the two cars is 3/2 meters, and the team travels 50 meters per minute on average. The time it takes for this train team to pass through the square with a length of 546 meters is 16 minutes, so a = _ _ _ _ _ _ _.

Third, solve the equation:

1、 2、

3、 4、

5、 6、

7、 8、

9, known as the root of the equation, find the value of the algebraic expression.

Four, the column equation to solve the application problem:

1, the enemy fled at the station 8 kilometers away from our army, and the time was 4 o'clock in the morning. Our army set off at 5 o'clock and pursued at the speed of 10 kilometer per hour, and finally caught up at 7 o'clock. What was the speed of the enemy when it fled?

2. In the mid-term examination, the information technology teacher asked each seventh-grade student to finish an article in 40 minutes. It is known that it takes 50 minutes for Xiaobao to finish an article of the same size independently, and only 30 minutes for Beckham. In order to complete the task, Xiaobao asked Beckham for help and cooperation after playing for 30 minutes. Can he finish it in the required time?

3. After learning "Operation of Rational Numbers", five students from each class in the seventh grade of the experimental middle school were selected to form a team, and a knowledge contest was held under the organization of the math teacher. The rules of the contest were: each team gave 50 questions respectively, and scored 3 points for answering one question correctly. (1) If the team of Class 2 finally scored 142 points, how many questions did the team of Class 2 answer correctly? (2) Can the final score of the first team be 145? Please briefly explain the reasons.

4. A "Hope School" has built a four-story teaching building, each floor has six classrooms, and there are three doors (two front doors and a side door with the same size) entering and leaving the building. During the safety inspection, these three doors were tested: when a front door and a side door are opened at the same time, 400 students can pass through in 2 minutes, and if a front door can pass through 40 more students per minute on average than a side door.

(1) How many students can pass through a main entrance and a side door every minute on average?

(2) During the inspection, it was found that the efficiency of going out was reduced by 20% due to the crowded students in an emergency. According to the safety inspection regulations, the students in the whole building should be evacuated safely through these three doors within 5 minutes in an emergency. Assuming that there are at most 45 students in each classroom of this teaching building, Q: Do these three doors meet the safety regulations? Why?

5. Mother Black Bear wants to test the effect of Little Bear's learning "solving application problems with equations", and gives Little Bear 19 apples, asking Little Bear to divide them into four piles. After the division, if the first pile is doubled, the second pile is increased by one, the third pile is reduced by two, and the fourth pile is doubled, the number of apples in these four piles should be the same. How should Little Bear divide this?

6. The school is going to spend 2,000 yuan to buy prizes for 22 students who won the Hope Cup competition. The first prize will be awarded to 200 yuan and the second prize to 50 yuan. How many students will win the first prize and the second prize respectively?

7. A store will raise the cost price of a commodity by 40% and then mark it. During the New Year's Day, it wants to sell it at a 20% discount to thank new and old customers for their patronage. The price is 224 yuan. What is the cost price of this commodity?

8. Party A and Party B went from school to the exhibition hall, which is 1000 meters away. After Party A left for 5 minutes, Party B set off. The speed of Party A was 80 meters/minute, and the speed of Party B was 180 meters/minute. How long will it take for Party B to catch up with Party A? How far is it from the exhibition hall when catching up with A?

Higher requirements:

1, known, then the algebraic value.

2. (200 1 year middle school entrance examination in Wuxi city, Jiangsu province) According to the market information, a shopping mall adjusted the price of two existing air conditioners of different models in the shopping mall, in which one air conditioner was sold at a profit of10% (relative to the purchase price), while the other air conditioner was sold at a loss of10% (relative to the purchase price).

(a) neither profit nor loss (b) profit1%(c) loss of 2% (d) loss1%.

3. A developer sells his house by installment, and Xiao Ming's family bought a new house with the current price of120,000 yuan. When buying a house, they need to pay a down payment of 30,000 yuan (in the first year). From the second year onwards, the annual house payment payable is 5,000 yuan plus the interest of the remaining arrears in the previous year. It is known that the annual interest rate of the remaining amount is 0.4%. In what year does Xiaoming's family need to pay 5,200 yuan?

4. There are 9 tons of fresh milk in a milk processing factory. If fresh milk is directly sold in the market, the profit per ton will be 500 yuan. If yogurt is sold, the profit per ton will be 1200 yuan; If it is made into milk tablets for sale, it can make a profit of 2000 yuan per ton.

Scheme 1: make as many pieces of milk as possible, and sell the rest directly;

Scheme 2: Make part of it into milk slices and the rest into yogurt for sale, and it will be completed in exactly 4 days;

(1) Which scheme do you think is the most profitable? Why?

(2) What questions can you ask after this problem is solved? If not, write down your problems?

5. Two cars start from the same place at the same time and drive in a straight line at the same speed in the same direction. Each car can only take 24 barrels of gasoline at most, and no other oil can be used on the way. Each barrel of oil can make a car move forward 60 kilometers. Both cars must return to the starting place, but they can return at different times. Both cars can borrow each other's oil. In order to make one of the cars as far away from the starting point as possible, how many kilometers away from the starting point should the other car return? How many kilometers has the car farthest from the starting place traveled?