(2): Change the width in the title from 4 cm to 3 cm, 2 cm, 1 cm, 0 cm (that is, the length and width are equal). What's the change in the rectangular area? Please compare the area of each rectangle obtained from this and think about whether you can enclose a rectangle with a larger area.
Direct formula
(1) Let the length be x.
(X+X-4)*2=20
2X= 14
X=7
It is 7 cm long and 3 cm wide.
Area: 3*7=2 1 (square centimeter)
(2) The rectangular area is getting less and less, and the square area is the largest.
One-dimensional linear equation application test questions (volume A)
I. Fill in the blanks (3 points for each small question, *** 18 points)
1. The sum of consecutive even numbers is 24. If the number in the middle is X, the other two numbers are _ _ _ _ _ _ _ and _ _ _ _ _ _. Countable equation: _ _ _ _ _ _ _ _ _, the solution is X = _ _ _ _ _ _
As we all know, if a color TV set is sold at a 10% discount on the list price, it can still make a profit of 20%. If it is known that the purchase price of a color TV set is 2400 yuan per set, the price tag is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
3. Fold a wire with a length of 12m into a rectangle.
(1) When the length is twice the width, the length is _ _ _ _ _ _ _ meters and the width is _ _ _ _ _ _ _ meters.
(2) when the length is three times the width, the area is _ _ _ _ _ _ _ square meters.
(3) When the rectangle is square, the area is _ _ _ _ _ _ _ square meters.
Someone has some money in the bank, and the known annual interest rate is 2.25%. Three years later, after deducting 20% interest, the after-tax interest can just buy a DVD player worth 720 yuan, so that that person has _ _ _ _ _ _ yuan in the bank.
5. There are two barrels of water, with barrel A containing180l and barrel B containing150l. To make the volume of bucket A twice that of bucket B, you should pour _ _ _ _ _ _ _ water from bucket B to bucket A. 。
6. Within the elastic range, the spring will be stretched by 0.5 cm per kilogram. If the original length of the spring is 65,438+02 cm, the length of the spring is 65,438+07 cm when the weight of _ _ _ _ _ _ _ _ is hoisted.
Second, multiple-choice questions (3 points for each small question, ***24 points)
7. It takes 12 minutes for classmate A to clean the classroom, and 9 minutes for classmate B. What is the time for two students to clean the classroom together?
A.2 1 min B. 10.5 min C.3 min D.36/7 min
8. Party A and Party B leave from the same place and go to a certain place. If Party A leaves for 2 hours first, then Party B catches up and catches up with Party A after 3 hours, the following statement is correct.
A.they both walked the same distance. B.b. goes further than a.
C.b walks 2 hours longer than A. None of the above answers are correct.
9. One day, a store sold two different calculators, both of which were sold to 64 yuan, but one of them earned 60% and the other lost 20%. In this transaction, the store.
A. earned 8 yuan B. lost 9 yuan C. didn't lose D. earned 24 yuan.
10. In order to respond to the call of "returning farmland to forest" and change the present situation of soil erosion, a farm carried out "returning farmland to forest" on 200 1. After returning farmland, the forest farm area is 25% of the cultivated land, with 160 hectares of forest farm and cultivated land. Assume that the forest farm area after returning farmland is X hectares.
A.25%= 160-x B。
25% x = 160d .( 1+25%)x = 160
1 1. A five-digit number, the first three digits are A and the last two digits are B. If the last two digits are put in front of the three digits A to form a new five-digit number, this new five-digit number is
a . b+a b . 100 a+b c . 100 b+a d . 1 1000 b+ 1 1 1a
12. A factory originally planned to produce A pieces every day, but now it produces more B pieces every day, so the number of days to produce M pieces in advance is
A.- Boston
13. There is a football made of 32 pieces of black and white cowhide. Black leather can be regarded as a regular Pentagon and white leather as a regular hexagon. If there are x pieces of white leather and (32-X) pieces of black leather. The correct equation is
a . 3x = 32 x b . 3x = 5(32 x)c . 5x = 3(32 x)d . 6x = 5(32 x)
14. If someone deposits 5,000 yuan for three-year education savings (interest tax is exempted), the principal and interest are 54 17 yuan, so the annual interest rate of this savings is
A 2.22% B 2.58% C 2.78% D 2.38%
Three. Short answer questions (***58 points)
15.(9 points) Store A has 100 color TV sets, and Store B has 88 color TV sets. Now a new store C has been opened, and 50 color TVs have been transferred from stores A and B, so that the remaining color TVs in stores A and B are equal. How many sets have been transferred in these two stores?
Solution: The equation relationship used to establish the equation in this question is _ _ _ _ _ _ _.
Suppose: If X TV sets are transferred from Store A, then _ _ _ _ _ _ _ TV sets are transferred from Store B, as follows.
Transfer the original color TV to the rest.
Jia shop
B branch
List the solutions of the equation _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
16.(9 points) A literary and art group organized a benefit performance for the "Hope Project" fundraising. There are two kinds of tickets for sale, one is an adult ticket to 8 yuan, and the other is a student ticket to 5 yuan. * * * Sold 1000 tickets with a fare of 6950 yuan. Q: How many tickets have been sold for each of these two kinds of tickets?
Solution: The equation established in this question has an equal relationship: adult ticket+student ticket = 1000 ① or adult ticket+student ticket = 6950 yuan ②.
Method 1: If X student tickets are sold, then _ _ _ _ _ _ adult tickets are sold, and then _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Method 2: If the student ticket is Y yuan and the adult ticket is _ _ _ _ _ _ _ _
One more question: If the ticket price remains unchanged, then the profit from selling 1000 tickets may be 7000 yuan? Why?
17.( 10) Give candy to a group of children. If each child has six, it is still short of 17. If each child has five, there will be three left. Q: How many children are there in this group? * * * How many sweets are there?
18.( 10 minute) For a three-digit number, the number on the hundredth digit is 1, and the number on the single digit is three times less than the number on the tenth digit minus two. If the order of the three digits is reversed, the sum of the three digits and the original three digits is 1 17 1.
19.( 10 minutes) From A to B, the bus used to take 7 hours. After the opening of the expressway, the average speed has increased by 20 kilometers per hour, and it takes only 5 hours to get there. Find the distance between a and B.
20.( 10) Please recall the process of solving application problems with arithmetic and equations. Which method do you think is better? Please give two examples to illustrate.
Reference answer
1.1.x-2x+23x = 2486,8,10 2.3200 3.14225.30000.000000000005
5.40 6. 10
Ii. 7.d8.A9.a10.b1.d12.b13.b14.c.
3. 15. The surplus color TV sets in two stores are equal, 50-x, 100-x = 88-(50-x), and x = 3 1. Store A transfers 3 1 and Store B transfers 19.
16. Method 1: 1000-x, 5x, 8 (1000-x)
5x+8( 1000-x)=6950，350，350，650
Method 2: 6950-y,
= 1000, 1750,650,350
No way. Let's assume that the number of student votes sold is Z, which is 5z+8 (1000-z) = 7000 according to the meaning of the question.
Solution: Z = is not a positive integer, so it doesn't matter.
4. 17. Suppose there are X children. The countable equation is 6x- 17 = 5x+3.
The result is x = 20.
18. Let ten digits be x, then the hundredth digit is X+ 1, the unit digit is 3x-2, and the countable equation is:
100(x+ 1)+ 10x+(3x-2)+ 100(3x-2)+ 10x+(x+ 1)= 1 17 1
The result of the solution is x = 3.
The three digits are 437.
19. let the distance between a and b be x kilometers, and the equation listed is (+20) × 5 = X.
Solution: x = 350
20.
One-dimensional linear equation application test questions (volume B)
I. Fill in the blanks (3 points for each small question, *** 18 points)
1.a and b run on a 400-meter-long circular track. It is known that A runs 9 meters per second and B runs 7 meters per second.
(1) Two people walk with their backs to the same place at the same time, and meet for the first time after _ _ _ _ _ _ _ seconds;
(2) Two people walk in the same direction at the same time and meet for the first time after _ _ _ _ _ _ _ seconds.
2. In order to improve the ecological environment and avoid soil erosion, a village actively planted trees. Originally, 60 trees were planted every day, but actually 80 trees were planted every day. As a result, the task of planting trees was completed four days in advance, so we planned to plant _ _ _ _ _ _ _ _.
3. A rope is used to form a square, and this rope is used to form a circle. It is known that the radius of a circle is 2 (π-2) meters smaller than the side length of a square. Can you tell me the length of this rope is _ _ _ _ _ _ _ meters?
4. A flower buys a 5 yuan branch. If it is sold at 20% of the listed price, 3 yuan can still make a profit. Ask about the price tag of each branch. If the listing price is X yuan each, the equation can be listed as _ _ _ _ _ _ _ _ _ _ _ _.
5. If the ten digits on a two-digit number are half of the single digits and the sum of the digits on the two-digit number is 9, then the two-digit number is _ _ _ _ _ _ _.
6. The current price of a drug is 56. 10 yuan, which is 15% lower than the original price, and the original price is _ _ _ _ _ _.
Second, multiple-choice questions (3 points for each small question, ***24 points)
7. It must be wrong for Li Bin to circle three adjacent numbers in a column of the calendar and calculate their sum.
A.20 B.33 C.45 D.54
8. A family of three will join a tour group. A travel agency told me that "adults buy full tickets and children are half price", and B travel agency told me that "family travel can be priced by group, that is, 20% off the full ticket per person". If the original prices of the two travel agencies are the same, then
A.a is more advantageous than B.
The discounts of C.A. and B. D. Which one is more favorable depends on the original price.
9. When the upwind speed of the aircraft is X km/h and the wind speed is Y km/h, the downwind speed of the aircraft is
A.(x+y) km/h
C.(x+2y) km/h (2x+y) km/h
10. One-meter-long teams advance at a speed of 60 meters per minute. It takes 1 minute for a classmate at the end of the line to walk from the end to the head of the line. The distance this classmate walks is
A.A meter B. (A+60) meter C.60a meter D.M.
1 1.a project is completed by itself 10 days, and B's work efficiency is twice that of A. Two people worked together for m days, but the remaining workload was completed by B. How many days will it take?
A. 1-( + )m B.5- m
None of the above is true.
12. A mountain road, someone walks from the mountain to the top of the mountain for 3 hours, and there is still 1 km to the top of the mountain. If it takes only 150 minutes to walk from the top of the mountain, it is known that the downhill speed is 1.5 times of the uphill speed. Let the uphill speed be x km/min, then the equation listed is
a . x- 1 = 5( 1.5x)b . 3x+ 1 = 50( 1.5x)
c . 3x- 1 =( 1.5x)d . 180 x+ 1 = 150( 1.5x)
13. The price of a commodity is one yuan. After the price is reduced by 10%, the price is reduced by 10%, and the sales volume increases sharply. The store decided to raise the price by 20% again. After the price increase, the price of this product is as follows:
A.a yuan B. 1.08a yuan C.0.972a yuan D.0.96a yuan.
14. According to the individual income tax regulations, citizens whose monthly salary does not exceed that of 800 yuan need not pay taxes, and those who exceed that of 800 yuan need to pay taxes by installments. The specific tax rates are as follows. If someone pays taxes in 80 yuan in 12, his monthly salary is.
Monthly Taxable Amount Tax Rate (%)
No more than 500 yuan.
Full 500 yuan to 2000 yuan 10.
More than 2000 yuan to 5000 yuan 15
…… ……
A 1900 yuan B 1200 yuan C 1600 yuan D 1050 Yuan.
Three. Short answer questions (***58 points)
15.( 13) Circle a plane figure with 40 cm long iron wire. (1) If a square is closed, its side length is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
(2) If a rectangle with a length of 12 cm is enclosed, its width is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
(3) If it is enclosed by a rectangle 5 cm wide, its length is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
(4) If a circle is enclosed, the radius of the circle is _ _ _ _ _ _ _ and the area is _ _ _ _ (π takes 3. 14, and one decimal place is reserved).
(5) Guess: ① If the perimeter is constant, if the surrounding figure is rectangular, the area of the rectangle will become more and more _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ② When the perimeter is constant, the area of the closed plane figure is the largest.
16.(9 points) In the volleyball match of middle school students in a city, according to the score of 2 points for winning a game, 0 points for drawing a game and 0 points for losing a game, the No.4 volleyball team in the city participated in 8 games and remained unbeaten. * * * 13. How many games did it win?
17.(9 points) Xiao Zhao and Xiao Wang had an exchange activity during the summer vacation. Xiao Zhao said, "I went to a week-long technology summer camp. The sum of the dates of these seven days is 84. Do you know what date I went out? " Xiao Wang said: "I went to my uncle's house for seven days during the holiday, and the date and number of months were also 84." Guess what date I went home? " Try and list the equations to solve the problem between Xiao Zhao and Xiao Wang.
18.(9 points) Collect a batch of saplings in each class, as follows: 100 saplings and surplus in the first class, 200 saplings and surplus in the second class, 300 saplings and surplus in the third class ... Finally, collect all saplings, and the number of saplings in each class is equal. Find the total number of saplings and classes.
19.(9 points) Li Hong bought a notebook for the whole class as a prize at the party. When he came back, he handed the account to Liu Lei, a member of the Life Committee, and said, "* * * bought 36 copies of two specifications, and the unit price was 1.80 yuan and 2.60 yuan respectively. I took 100 when I went, and now I get 27.60 back. " Liu Lei counted. Think about whether it is possible to get 27.60 yuan back, and try to explain it with the knowledge of the equation.
20.(9 points) The extracurricular table tennis team in Class Four, Grade One bought two pairs of table tennis boards. If everyone pays 9 yuan, it will cost 5 yuan more. If everyone pays 8 yuan, there will be 2 yuan less. Please ask questions according to the above situation and solve the equations in parallel.
Reference answer
I. 1. ( 1)25 2 200 2.960 3.8π4.80% x = 5+3 10 5.36 6.66
2. 7.A8.B9.c10.b1.b12.d13.c14.c.
Three. 15. (1)1000 (2) 8 964 (3)157510 (4) 6.4128.6 (5) Great Circle.
4. 16. Assuming that X field is won, the equation can be listed: 2x+(8-x) = 13, and the solution is x=5.
17. Xiao Zhao went out on the 9th, and Xiao Wang went home on July 15 (hint: if the number of days in the middle of seven days is X, the other six days are X-3, X-2, X- 1, x+ 1, x+2, X. So the number of months is also a multiple of 7, which means the number of months is 7. I stayed at my uncle's house from the 8th to14th, so I went home on15th.
18. 9 classes of saplings ***8 100. (Hint: There are many ways to establish the element equation in this question. The total number of saplings can be set as x, and the equation can be set by the equal number of saplings of the first and second types:
100+(x- 100)= 200+〔x-200- 100-？ 6? 1 (x- 100)]
100(x- 1)+x = 100 x If you notice that 100 (x-1) trees in the penultimate class are less than100x trees/kloc-0.
19. Buy 24 notebooks at a unit price of 1.80 yuan and 2 notebooks at a unit price of 2.60 yuan 12. If the price of Li Hongbao is the original price, we buy X notebooks with a unit price of 1.80 yuan, and get the following equation: 1.8x+2.6? 6? 1(36-x)= 100-27.60，
The solution of x = 2.60 does not conform to the meaning of the actual problem, so it is impossible to get back 27.60 yuan.
20.
Full-chapter test for linear equations with one variable (1)
Fill in the blanks
(1) If 4 is the solution of equation 3a-5x=3(x+a)+2a about x, then a = _ _ _ _ _ _
(2) It is known that the solution of the equation about y is y=-8, so the value of _ _ _ _ _.
(3) When x = _ _ _ _ _ _, the single sum belongs to the same category.
(4) When a is _ _ _ _ _, the equation about X is a linear equation.
(5) When m is _ _ _ _ _ _, 2 is the solution of the equation about X. ..
Second, multiple choice questions
(1) Among the following types, () is a linear equation.
3x-7
(2)
(3)
(D)4x-3=2(x+ 1)
(2) It is correct to express the quantitative relationship that "the number 5 greater than x equals 2" by equation.
(A)2+x=5
x-5=2
x+5=2
5-x=2
(3) The solutions of the two equations in the following groups are the same ().
(A)3x-2= 10 and 2x- 1=3(x+ 1)
(B)4x-3=2x- 1 and 3( 1-x)=0.
And 3x+ 1-2x=6.
(D)-4x- 1=x，5x= 1
(4) The following equation without brackets is correct ().
(a) x- 12-2x=5 from 2x-3(4-2x)=5.
(b) 2x- 12-6x=5 from 2x-3(4-2x)=5.
(c) 2x- 12+6x=5 from 2x-3(4-2x)=5.
(d) 2x-3+6x=5 from 2x-3(4-2x)=5.
Third, solve the following equation
( 1) 。
(2) 。
(3) 。
(4) 。
(5) 。
(6) Solve Equation 5(x+2a)-a=2(b-2x)+4a about x.
Fourth, answer questions.
(1) When x=2 is known, the value of the algebraic expression is 10. Find the value of x=-2 times number expression.
(2) If |2(x-3)-(3x+4)|=5, find the value of x.
(3) known, verified: x = y.
Answers and tips
One,
( 1)a =- 16； (2)a= 14，； (3)x = 2； (4) ; (5)m= 4 .
Second, (1) d; (2)C； (3)B； (4) c
( 1); (2)x = 1； (3) ;
(4) ; (5) ; (6) ;
( 1)-2; (2)x= 15 or x =-5; (3) ellipsis.