volume one
Fill in the blanks
1. If the sum is reciprocal, then a is equal to.
2 is the solution of the equation, then
3. So, the equation
4. If it is about a linear equation, then
5, in the equation, known, then
6. Party A and Party B walk in opposite directions in A and B, with a distance of 10 km. Party A walks x kilometers per hour and Party B walks 2x kilometers per hour. When they start at the same time 1.5 hours later, the equation can be obtained.
7. Deposit 1 0,000 yuan in the bank with a term of 2 years and an annual interest rate of 5%. After the expiration, after deducting 20% interest tax, you can get back the RMB principal and interest.
8. If the monomial is a similar project, then
9. After the price of a certain brand TV set was reduced by 10%, the price per set was 2430 yuan, so the original price of this color TV set was RMB per set.
10, there are two buckets of water, bucket a has 180 liters of water, and bucket b has 150 liters of water. In order to make the volume of water in bucket A twice that of bucket B, water should be poured into bucket A from bucket B. ..
Second, multiple choice questions
1, among the following equations, () is a linear equation.
A, B, C, D,
2. The same equation as the solution of the equation is ()
A, B, C, D,
3, if the equation is a linear equation, then the solution of this equation is ().
A, B, C, D,
4. A group of 328 teachers and students travel by bus, and the existing school bus can take 64 people. If you rent a bus, each car can take 44 people, so how many cars should you rent? In this problem, if you want to rent a bus, the equation can be listed as ()
A, B, C, D,
Xiaoming accidentally polluted a constant in the equation when he was solving it. He can't see clearly The equation of pollution is: What? Xiao Ming thought for a moment, and then looked at the answer at the back of the book. The solution of this equation is that this constant is completed quickly and the homework is completed quickly. Students, can you make up this constant? It should be ()
a、 1 B、2 C、3 D、4
6. It is known that if there is a maximum, the solution of the equation is ().
7. After the equation is named, the correct one is ().
A, B, C, D,
8. A commodity is sold at a 10% discount twice in a row. After the price reduction, the price of each commodity is RMB, and the original price of the product is ().
A, yuan b, yuan c, yuan d, yuan
9. The length of a rectangle is four times the width of 2 cm. If the length is cm, then the width is () cm.
A, B, C, D,
10, if they are opposites, then (). a、 10 B 、- 10 C、D、
Third, answer questions.
1、 2、
3、 4、
5、 6、
Fourth, answer questions.
1, known, if ①, the value of; (2) When any value is taken, it is small; (3) When taking any value, are they opposite numbers?
2. The known one-dimensional linear equation, try to find the value, and solve this equation.
3. If, find the value of.
4, if about the value of.
5. Think about it: You must be a strong man in life!
1. There are 85 skilled workers in a workshop, and each person can process 16 parts A or 10 parts B on average every day. Two type A parts and three type B parts make a set. How many people are arranged to process the A-shaped parts and the B-shaped parts respectively to make the A-shaped parts and the B-shaped parts processed every day just match?
2. A school in our city planned to donate 3,500 books to students in western mountainous areas, and actually donated 4 125 books. Among them, junior high school students donated 120% of the original plan, and senior high school students donated 1 15% of the original plan. How many copies did junior and senior high school students donate more than originally planned?
Chapter VI One-dimensional Linear Equation Test Questions
Volume b
Fill in the blanks
1, the solution of the equation is.
2. if, then a=
3. If +8=0 is a linear equation, then m=.
4. If the reciprocal of is equal to, then x- 1=.
The sum of the ages of mother and daughter this year is 53 10 years ago. It is known that the mother's age was 10 times that of her daughter before 10. If the daughter's age before 10 is x, it can be expressed by an equation.
6. If A and B are the numbers in the tenth and fourth place of a two-digit number respectively, then the two-digit number after the number in the tenth place and the number in the fourth place are reversed is.
7. The equation is represented by an algebraic expression containing X, and X is represented by an algebraic expression containing Y. ..
8. If both the equation and the equation are homogeneous solutions, then k=.
9. If the monomial and 9a2x- 1b4 are similar terms, then x=.
10, if sum is the opposite number, the value of x-2 is.
Second, multiple choice questions
1, which belongs to the linear equation in the following categories is ().
A, B, C, D,
2. According to equation (), "the sum of 3 times of x and 5 is 2 more than x".
A, B, C, D,
3. When solving the equation, turn the denominator into an integer and get ().
A, B,
C, D,
4. The ratio of three positive integers is 1: 2: 4, and their sum is 84, so the largest of these three numbers is ().
a、56 B、48 C、36 D、 12
5. When the solution of the equation is-1, the value of k is ().
a、 10 B 、-4 C 、-6 D 、-8
6. According to national regulations, individual income tax shall be paid in 800 yuan for employees whose monthly salary exceeds 20%. Xiaoying's mother's salary in June was 45.89 5438+ 10/0, and Xiaoying's mother's salary in June was ().
A, 8045.49 yuan b, 1027.45 yuan c, 1227.45 yuan d, 1045.9 yuan.
7. A young singer grand prix held in a city, this year, there were * * A participants, and the number of participants increased by 20% compared with last year, with three more people. If the number of participants last year was X, then X is ().
A, B, C, D,
8. A businessman sold two clothes at the price of 120 yuan, one made a profit of 25% and the other lost 25%. In this transaction, the businessman ().
A, earn 16 yuan b, compensate 16 yuan c, don't earn, don't compensate d, uncertain.
9. A worker originally planned to produce A pieces every day, but now he actually produces B pieces every day, so the number of days to produce M pieces in advance is ().
A, B, C, D,
10, it takes a day and b days to complete a project, so it takes two people to work together ().
A, B, C, D,
Third, solve the equation
1、 2、
3、 4、
Fourth, answer questions.
1 and y= 1 are the solutions of the equation. Find the solution of the equation about x ..
2. the solution of the equation and the solution of the equation about x are reciprocal, and the value of k is found.
3. It is known that x=- 1 is the solution of the equation about x, so find the value of 5.
Fifth, solve application problems with column equations.
1. Generally speaking, ships sail in the water. When the current speed is known as 10 km/h, the speed of the ship in still water is 40 km/h, how many hours does it take for the ship to sail back and forth between A and B? If the time required in this problem is set to x hours, what conditions need to be added to solve the equation? According to your idea, add conditions and solve parallel equations.
2. A factory originally planned to produce a batch of parts in 26 hours, but it took 24 hours to produce five more parts per hour, which not only completed the task, but also produced 60 more parts than originally planned. How many parts were originally planned to be produced?
3. The sum of the unit prices of A and B is 65,438+000 yuan. Because of seasonal changes, the price of commodity A decreased by 65,438+00% and that of commodity B increased by 5%. After the price adjustment, the sum of the unit prices of commodities A and B increased by 2% compared with the original plan. What is the original unit price of A and B?
The speed of the car is 28 kilometers per hour when going uphill and 35 kilometers per hour when going downhill. Downhill is 2 times less than uphill 14 km, and it takes 12 minutes to return to the original road. How many kilometers do you want to go uphill and downhill?
5. Two groups of Party A and Party B *** 120 people travel to a scenic spot. The scenic spot stipulates that groups with more than 80 people can buy group tickets. It is known that each group has a discount of 20% over individual tickets, and both groups have less than 80 people, so the two groups decided to buy them together.
Group tickets, * * * discount 480 yuan, then how many group tickets per person?
Reference answer: Chapter VI One-variable Linear Equation Volume A
1. 1,-12,3, -3 or 9 4,15,506, 1.5(X+2X)= 10 7,/kloc-.
9,270010,40 (hint: suppose you want to pour x water from bucket b to bucket a, then it is: 180+ x =2( 150- x) to get x =40).
2. 1-5 A，B，A，B，C 6- 10 A，B，D，D，C。
Three. 1, 2, x =-4 3, 4, 5, x = -9 6, x =4 or -2.
Iv. 1, (1)
2、a=-2 X= -6
3、XY=-4
4. (Note: If the term Y is not included, the coefficient of Y is equal to 0, and the combination of similar terms is: (6-3R)X+(5-2R)Y-2+4R=0, that is, 5-2R=0, ∴).
5. 1, 25 60 (hint: if there are x people doing part A, then there are (85-X) people doing part B, then the solution given by 3× 16X=2× 10(85-X) is: x = 25 85-.
2, 400 volumes, 225 volumes (assuming that junior high school students originally planned to lose X books, then120 ﹪ x+115 ﹪ (3500-x) = 4125) Solution:
Chapter VI One-variable Linear Equation Volume B
1. 1, 2, a=-2 or -4 3, m= 1 4, X=0 5, 33 years old 10X+X=33 6,10b+a.
7,9, X=2 10, (Cuo: from the meaning of the question: 5X+2+(-2X+9)=0, so X=- then x-2 =-2 =-)
Second, 1, C 2, B 3, B 4, B 5, C 6, B 7, C 8, B 9, B 10, c.
Three. 1，2，X=4 3，Y= -2 4，X= - 1。
4. 1X=-2 (Cuo: solution: substitute Y= 1 into equation 2-(m-Y)=2Y to get m =1; Then substitute m= 1 into the equation m(X+4)=2(mX+3) and get: X=-2).
2、R= 1 3 、-23
V. 1 omitted
2.780 pieces (counting: assuming that X pieces were originally planned to be produced, if yes, the solution is X=780).
3.20 yuan and 80 yuan (hint: if the original unit price of commodity A is X yuan and the original unit price of commodity B is (100-X) yuan, then (1-kloc-0/0%) x+(100-x) (/kloc)
4.42km, 72km (when it is set to go uphill x km, it will go downhill (2X- 14) km,
Then: X=42 2X- 14=70)
5, 16 yuan (Hint: If each group ticket is X yuan, then each individual ticket in Bird is available.
120×- 120 x = 480:x = 16)
One-dimensional linear equation exercise
Basic question:
First, multiple-choice questions:
1, which belongs to the linear equation in the following categories is ().
A.B.
C.D.
2, the solution of the equation is ()
A. BC 1
3. If the solution of the equation about satisfies the equation, the value of is ().
A. 10 8th century BC.
4, according to the following equation property is correct ()
A. Fuck, get B. Fuck, get
C. pass, get D. pass, 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 twice in a row 10%. After the price reduction, the price of each TV set is one yuan, so the original price of TV set is ().
A.0.8 1a yuan B. 1.2 1a yuan C.D.
8. A store sells two pieces of clothes, each 60 yuan, one earns 25% and the other loses 25%. Then after these two 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, in the following equation, belongs to the 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 may not be true ().
(A) (B)
(C) (D)
12, the solution of the equation is that 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 variation, the correct is ().
(1) Equation, shift term, get
(b) Equation, without brackets, gives
(c) Equation, which converts the unknown coefficient into 1 to obtain
Formation of equation
15. Son 12 years old, father 39 years old. The father is four times as old as his son.
(a) Three years later; (B)3 years ago; Nine years later; No way.
16. The football used by chongqing lifan New Feeling Football Team for training is made of 32 pieces of black and white cowhide, of which the black leather can be regarded as a regular pentagon and the white leather as a regular hexagon. The ratio of black and white leather blocks is 3:5, and the number of black and white leather blocks is required. If the number of black leather blocks is 0, the listed equation is correct ().
(A) (B)
(C) (D)
17, Coral Middle School built a comprehensive building, leaving a rectangular open space with a length of more than 5m and a circumference of 50m. In order to beautify the environment, the school decided to plant it as turf. It is known that the minimum planting cost per square meter of turf is RMB, so planting turf needs at least ().
(1) Yuan; (b) yuan; (c) yuan; (4) yuan.
One year, two years, three years.
2.25 2.43 2.70
18. The annual interest rate of bank education savings is shown in the following table:
Xiaoming is in grade seven now. In July this year, his parents deposited 30 thousand yuan in the bank for him to use when he was in high school three years later. After three years, the income will be maximized, and Xiao Ming's parents should adopt ().
(a) Direct deposit for three years;
(b) Deposit first 1 year, and after 1 year, the total interest will be automatically transferred to the 2-year period;
(c) Deposit one 1 year, and after 1 year, automatically transfer the principal and interest to two 1 year;
(d) Deposit a 2-year deposit first, and after 2 years, the total interest will be automatically transferred to 1 year deposit.
2. Fill in the blanks:
1, then _ _ _ _ _.
2, known, then _ _ _ _ _ _ _.
3. If the solution of the equation 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 people in Class A and Class B, and Class A has 2 more people than Class B, so Class B has _ _ _ _ _ _ _ _.
6. A number is twice as big as its half. If a number is set to, the equation is _ _ _ _.
7. When _ _, the values of algebraic sum are opposite.
8, 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 on the right, it is the calendar of 65438+February 2003. At present, four numbers are arbitrarily framed by a rectangle in the calendar.
Please use an equation to express the relationship between _ _ _ _ _ _ _ _.
10, a long cylindrical test tube with an inner diameter of 3㎝, which is filled with water. Now gradually drop the water in the test tube 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 water in the test tube drops.
1 1. During the National Day, New Century Department Store has a seasonal discount. Jane bought a sportswear at a 20% discount, saving 16 yuan, so he actually spent _ _ _ yuan on this dress.
12, the total length of chengdu-chongqing railway is 504 kilometers. An express train leaves Chongqing at a speed of 90 kilometers per hour. 1 hour later, another local train departed from Chengdu at a speed of 48 kilometers per hour. Then the two trains meet _ _ hours after the local train leaves (regardless of the stop time along the way).
13. When we were young, we heard the story of the race between the tortoise and the hare. We all know that the tortoise finally defeated the white rabbit. If in the second race, the white rabbit is ashamed and brave, and catches up with the tortoise at the speed of 10 1 m/min when it is behind the tortoise, and the tortoise still crawls at the speed of 1 m/min.
14, the annual interest rate of one-year fixed deposit is 1.98%, and 20% interest must be deducted as interest tax and turned over to the state treasury. If Xiaoying deposits a one-year time deposit, and the interest after tax is 158.4 yuan, then the RMB she deposits is _ _ _ _ _
15, 52 cars lined up in two teams, each car was one meter long, and the distance between the two cars was 3a/2m. The average speed of the team was 50 meters per minute. It takes 16 minutes for this train to pass through the 546m long square, so a = _ _ _ _ _ _ _
Third, solve the equation:
1、 2、
3、 4、
5、 6、
7、 8、
9. Knowing the root of the equation, find the value of the algebraic expression.
Four, column equation to solve application problems:
1. The enemy escaped at the station 8 kilometers away from our army. The time is 4 am. Our army set off at 5 o'clock and pursued at the speed of 10 km per hour. And I caught up at 7: 00. What is the speed at which the enemy fled?
In the mid-term exam, the information technology teacher asked every seventh-grade student to write an article within 40 minutes. As we all know, it takes Bao Xiao 50 minutes to finish an article of the same size independently, while Beckham only needs 30 minutes. In order to complete the task, Bao Xiao 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 of the seventh grade in 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 game are: each team will give 50 questions respectively, and get 3 points for answering one question correctly. (1) If the team in Class Two finally got 142, how many questions did the team in Class Two answer correctly? (2) Can the final score of the first team be 145? Please briefly explain the reasons.
A "Hope School" has built a four-story teaching building with six classrooms on each floor, and there are three doors (two front doors and a side door of the same size) in and out of 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, in case of emergency, students in the whole building should be evacuated safely through these three doors within 5 minutes. Suppose 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 wanted to test the effect of Little Bear's learning "solving application problems with equations", and gave him 19 apples to divide him into four piles. After dividing, 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 will be the same. How does the bear divide these 65400 apples?
6. The school is going to spend 2000 yuan to buy prizes for 22 students who won the Hope Cup competition. The first prize was awarded to 200 yuan, and the second prize was awarded to 50 yuan. How many students will win the first prize and the second prize respectively?
7. A store will increase the cost price of a commodity by 40%, and then mark it. During the new year's day, it wants to sell 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 visited the exhibition hall which is 0/000 meters away from the school. Party A leaves for 5 minutes before Party B leaves. The speed of Party A is 80m/min, and the speed of Party B is 180m/min. How long will it take Party B to catch up with Party A? How far is it from the exhibition hall when we catch up with A?
Higher requirements:
1, known, then the algebraic value.
2.(200 1 Senior High School Entrance Examination in Wuxi City, Jiangsu Province) According to the market information, a shopping mall has adjusted the prices of two existing air conditioners of different models. One air conditioner sold after price adjustment can make a profit of 10% (relative to the purchase price), while another air conditioner sold after price adjustment will lose 10% (relative to the purchase price).
(a) neither making a profit nor losing money; (b) 1% profit; 2% loss; 1% loss.
The developer sells the house by installment. Xiao Ming's family bought a new house, and the current price is 1.2 million. When buying a house, they need to pay a down payment of 30,000 yuan (the first year). Starting from the second year, the house payment should be 5000 yuan per year plus the interest on the remaining arrears of 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 5200 yuan?
A milk processing factory has 9 tons of fresh milk. If you sell fresh milk directly in the market, you will make a profit of 500 yuan per ton. If you sell yogurt, the profit per ton 1200 yuan. If it is made into milk tablets for sale, it can make a profit of 2000 yuan per ton.
Option 1: make as many pieces of milk as possible and sell the rest directly;
Option 2: part of it is made into milk tablets, and the rest is made into yogurt for sale, which is completed in exactly 4 days;
(1) Which scheme do you think is the most profitable? Why?
(2) What questions can be asked after this problem is solved? If not, write down your question?
Two cars start from the same place at the same time and drive straight in the same direction at the same speed. Each car can only take 24 barrels of gasoline at most, and no other oil can be used on the way. A barrel of oil can propel a car 60 kilometers forward. Both cars must return to the starting point, but they can return at different times. Both cars can borrow oil from each other. In order to make one car as far away from the starting point as possible, how many kilometers should the other car return from the starting point? How many kilometers has the car farthest from the starting point traveled?
1. Generally speaking, ships sail in the water. When the current speed is known as 10 km/h, the speed of the ship in still water is 40 km/h, how many hours does it take for the ship to sail back and forth between A and B? If the time required in this problem is set to x hours, what conditions need to be added to solve the equation? According to your idea, add conditions and solve parallel equations.