1, through the unremitting efforts of scientists, pi has been calculated to10111digits after the decimal point. Rewrite "19669 1" into a number with ""as the unit, and keep two decimal places (10.1100 million).

3. The two internal terms of a proportion are 0.7 and 30 respectively, and the product of the two external terms is (). If one of the external terms is 2. 1, then the ratio is ().

4. A number =2×3×A, B number =2×5×A, and given that the greatest common divisor of A and B numbers is 22, then A = (); If the least common multiple of a and b is 2 10, then A= ().

5. Xiaohong deposited 1000 yuan lucky money in the bank with a fixed term of 3 years and an annual interest rate of 2.25%. At maturity, Xiaohong can get the principal and after-tax interest of RMB ().

6, rectangular, its width is longer. If the width is increased by 12 cm, the rectangle becomes a square. It turns out that the area of a rectangle is () square centimeters.

7, cylinder and cone bottom radius and volume are equal, respectively, the height of the cone is 65438 0.5 decimeter, the height of the cylinder is ().

8. The decimal unit of (a (a is a non-zero natural number) is (), and there are () such decimal units. When a is (), this score is the smallest false score; When a is (), this score is the largest true score. The reciprocal of is ().

9. Cut a 9-decimeter-long cube into 2-decimeter-long cubes, and you can get at most () cubes.

10. The box contains several red balls and yellow balls of the same specification and quantity. Take out five red balls and three yellow balls at a time. After taking () times, the red ball disappeared, leaving six yellow balls. If you put the ball back in the box and take any ball of 1 in the box, the probability of touching the red ball is ()%. If you don't put the red ball back in the box, then if you take the 1 ball, the possibility of touching the red ball is ()%.

Two, true or false (***5 points)

1, 1 meter Increase it, then decrease the meter, and the result remains the same. ............................................................... ()

2.A and B are non-zero natural numbers, and A is equal to 40% of B, then A < B ................................. ()

The amount of money subscribed to decimal newspapers is inversely proportional to the number of copies. ………………………………………( )

February of the 2008 Olympic Games has 29 days. ……………………………………… ( )

5. The sum of any two odd numbers must be even, and the sum of any two prime numbers except 2 must also be even. ( )

Three, multiple choice questions (***5 points)

1, 0.85, 85. 1%, the four numbers are arranged from small to large, and the second place is ().

a、0.85 B、C、85. 1% D、

2. The ratio of the degrees of the three internal angles of a triangle is 1: 2: 3, and this triangle is ().

A, isosceles triangle b, acute triangle c, right triangle d, obtuse triangle

3. Xiaoming's home is about 1 km from school. It takes him about () minutes to walk from home to school.

a、80 B、60 C、5 D、3

4.a is the true score (a≠0), then a2 and 2a are compared. ( )

A, A2 > 2ab, A2 < 2ac, A2 = 2ad, which cannot be determined.

5. In order to clearly show the monthly output in the first half of the year and its changes, the TV factory should draw ().

A bar chart b line chart c fan chart

Four, calculation (***33 points)

1. Numbers written directly (8 points)

- = 4.9÷0.0 1= 7×0.8+0.2×7= 5.38-( 1.8+0.38)=

26× = 3. 14×32+3. 14= 0. 125× 16= 2.82÷0.5÷2=

2. Find the value of x (5 points)

x: 1.2=5:4

3. Off-model calculation (simple calculation is needed if it can be simplified) (12 points)

0. 125×3.2×250

4, column calculation (8 points)

1, the number a is 0.6 less than the number b, and the ratio of two numbers a and b is 1: 3. What is the sum of a and b?

2. 25% of a number is less than twice its 17.5. Find this number.

5. Draw, calculate and fill in. (***6 points)

(1) Draw a square with a side length of 4 cm on the right. ( 1)

(2) Draw the largest circle in the square. Draw on the map.

How did you find the center of the circle? ) (2 points)

(3) If you are in this square, cut off the circle and the rest.

What is the area of? (Column calculation, 2 points)

(4) The rest have () symmetry axis (1 point)

Six, the application problem (***3 1 point, the sixth question 6 points, the rest are 5 points)

1, Xiao Wang plans to finish reading an extra-curricular book in three days (the number of pages read every day). The first day went according to the original plan, and the next day he only read 50 pages because of the class reunion. In this way, he read half of the book in two days. How many pages are there in this book?

Master Wang wants to mow the school lawn, which is 6 square meters per minute and can be completed in half an hour. How long will it take to renovate 8 square meters per minute? (Use proportional solution)

3. Xiaoming needs 36 points to walk from home to school and 12 points to ride a bike. Eight minutes after he left home by bike, his car broke down and he had to walk. How long does it take Xiao Ming to get to school?

On a map with the scale of1:4,870,000, Xiaoming measured that the distance from Beijing to Shanghai was 30 cm. It is known that the fire travels at the speed of120km per hour. Grandma got on the bus at 7 pm on April 29th. When should Xiao Ming pick up the car?

5. In a cylindrical water storage bucket, put a cylindrical steel column with a bottom area of 78.5 square centimeters. If all of them are put into the water, the water surface will rise by 9 cm; If the cylindrical steel column is 8 cm above the water surface, the water surface will drop by 4 cm. Find the volume of cylindrical steel column. Responder: You are a handsome guy | Level 1 | 20 10-6- 18 20:55.

Go online to find the respondents: abcdwty | level 2 | 2010-6-1821:59.

Junior high school mathematics: comprehensive training of applied problems 1

1. Party A, Party B and Party C plant trees in two plots A and B respectively, with 900 trees in plot A and 0/250 trees in plot B. It is known that Party A, Party B and Party C can plant 24, 30 and 32 trees every day, of which Party A plants trees in plot B, and Party B plants trees in plot A first and then moves to plot B..

The total number of plants is 900+ 1250 = 2 150, and 24+30+32 = 86 plants can be planted every day.

The planting days are 2 150 ÷ 86 = 25 days.

If A completes 24× 25 = 600 in 25 days, then B will complete 900-600=300 trees before helping C.

That is, after 300 ÷ 30 = 10 days, I transferred from A to B on 1 1 day.

2. There are three grasslands with an area of 5 15 and 24 mu respectively. The grass on the grassland is as thick and grows as fast. The first grassland can feed 10 cows for 30 days, and the second grassland can feed 28 cows for 45 days. How many cows can eat on the third grass for 80 days?

This is a complicated problem of herding cattle.

The grass eaten by each cow every day is 1 serving.

Because the first piece of grassland with an area of 5 mu+grassland with an area of 5 mu = 10× 30 = 300 copies for 30 days.

Therefore, the amount of grass per mu and the amount of grass per mu for 30 days are 300 ÷ 5 = 60.

Because the original grass quantity of the second grassland with an area of 15 mu+the grass quantity of 65438 with an area of 45 days = 28× 45 = 1260.

Therefore, the amount of raw grass per mu and the amount of grass in 45 days per mu are 1260 ÷ 15 = 84 copies.

So 45-30 = 15 days, and the area per mu is 84-60 = 24.

Therefore, the area per mu is 24/ 15 = 1.6 parts/day.

Therefore, the amount of grass per mu is 60-30× 1.6 = 12.

The third plot, with an area of 24 mu, needs to grow 1.6× 24 = 38.4 parts per day, and the original grass has 24× 12 = 288 parts.

Every day, 38.4 cows need to eat the newly grown cows, and the remaining cows eat the original grass every day, so the original grass is enough for 80 days, so 288 ÷ 80 = 3.6 cows.

So a * * * needs 38.4+3.6 = 42 cows to eat.

Assume that the daily grazing amount of each cow is 1, and the total grass amount per mu for 30 days is10 * 30/5 = 60; The total grass yield per mu in 45 days is: 28*45/ 15=84, so the new grass yield per mu per day is (84-60)/(45-30)= 1.6, and the original grass yield per mu is 60-1.6 *.

Scheme 2: 10 cows eat 5 mu in 30 days, and 30 cows eat 5 mu in 30 days 15 mu. According to 28 cows eating15mu for 45 days, it can be deduced that15mu of new grass (28 = 45-30 * 30)/(45-30) = original grass quantity15mu:1260-24 *. 15mu cattle required for 80 days 180/80+24 (head) 24mu: (180/80+24) * (24/15) = 42 heads.

3. A project, contracted by both parties, can be completed in 2.4 days and needs to be paid 1800 yuan; Contracted by Team B and Team C, it can be completed in 3+3/4 days, and it needs to be paid 1500 yuan; Contracted by two teams, Party A, Party B and Party C, it can be completed in 2+6/7 days at a cost of 1.600 yuan. On the premise of ensuring the completion within one week, which team will spend the least?

The cooperation between Party A and Party B is completed in one day 1 ÷ 2.4 = 5/ 12, and the payment 1800 ÷ 2.4 = 750 yuan.

The cooperation between ethylene, propylene and Fang Yitian is 1 ÷ (3+3/4) = 4/ 15, and the payment is 1500× 4/ 15 = 400 yuan.

The cooperation between Party A, Party C and Fang Yitian is 1÷ (2+6/7) = 7/20, and the payment is 1600× 7/20 = 560 yuan.

Three people cooperate in one day (5/12+4/15+7/20) ÷ 2 = 31/60,

Three people cooperate to pay (750+400+560) ÷ 2 = 855 yuan a day.

Party A alone completes 31/60-4/15 =1/4 every day, and pays 855-400 = 455 yuan.

Party B alone completes 3 1/60-7/20 = 1/6 every day, and pays 855-560 = 295 yuan.

Party C alone completes 31/60-5/12 =110 every day and pays 855-750 = 105 yuan.

So by contrast,

Choose b with 1 ÷ 1/6 = 6 days, only 295× 6 = 1770 yuan.

There is a rectangular iron block in the cylindrical container. Now turn on the tap and pour the water into the container. In 3 minutes, the water surface is just above the top of the cuboid. /kloc-After 0/8 minutes, the container has been filled with water. It is known that the height of a container is 50 cm and the height of a cuboid is 20 cm. Find the ratio of the bottom area of a cuboid to the bottom area of a container.

Divide this container into upper and lower parts. According to the time relationship, it can be found that the volume of water in the upper part is 18 ÷ 3 = 6 times that of the lower part.

The height ratio of the upper half and the lower half is (50-20): 20 = 3: 2.

So the bottom area of the upper part is 6 ÷ 3× 2 = 4 times the bottom area of the lower part filled with water.

Therefore, the ratio of the bottom area of the cuboid to the bottom area of the container is (4- 1): 4 = 3: 4.

Unique solution:

(50-20): 20 = 3: 2, and when there is no cuboid, it takes 18*2/3= 12 (minutes) to fill 20 cm.

So the volume of a cuboid is 12-3=9 minutes of water, because the height is the same.

So the volume ratio is equal to the bottom area ratio, 9: 12 = 3: 4.

Two bosses, A and B, bought a fashion at the same price, and B bought 1/5 sets more than A, and then they sold them at profit margins of 80% and 50% respectively. After both of them were sold out, A still made more profits than B, just enough for him to buy 65,438+00 sets of this fashion, which A bought at the beginning.

Consider that the number of groups of A is 5 and the number of groups of B is 6.

The profit earned by A is 80% × 5 = 4, and the profit earned by B is 50% × 6 = 3.

A is 4-3 more than B = 1 copy, and this1copy is 10 set.

So, A initially purchased 10× 5 = 50 sets.

6. There are two water pipes A and B, and water is injected into two pools with the same size at the same time. At the same time, the water injection ratio of A and B is 7: 5. After 2+ 1/3 hours, the sum of the water injected into A and B is just a pool. At this time, the water injection rate of pipe A is increased by 25%, while pipe B remains unchanged.

Think of a pool of water as 1.

Because a pool of water was injected after 7/3 hours, 7/ 12 was injected into the A pipe and 5/ 12 was injected into the B pipe.

The water injection rate of a pipe is 7/ 12 ÷ 7/3 = 1/4, and that of b pipe is 1/4× 5/7 = 5/28.

The later water injection of a pipeline is1/4× (1+25%) = 5/16.

The time spent is 5/ 12 ÷ 5/ 16 = 4/3 hours.

It takes 1 ÷ 5/28 = 5.6 hours for tube B to fill the pool.

Water injection needs 5.6-7/3-4/3 = 29/ 15 hours.

That is 1 hour and 56 minutes.

Continue to do another method:

According to the original water injection rate, it takes 7/3 ÷ 7/ 12 = 4 hours to fill the pool with pipes.

The filling time of tube B is 7/3 ÷ 5/ 12 = 5.6 hours.

Time difference is 5.6-4 = 1.6 hours.

Later, the speed of nailing pipe increased, so the time was less and the time difference was more.

After the speed of A is increased, it takes 7/3× 5/7 = 5/3 hours.

The shortened time is equivalent to1-1÷ (1+25%) =1/5.

So the time is shortened by 5/3× 1/5 = 1/3.

So the second pipe needs1.6+1/3 = 29/15 hours.

Do it another way:

(1) The remaining nail tubes need time.

7/3× 5/7 ÷ (1+25%) = 4/3 hours.

(2) The time required to find the remaining B tubes.

7/3× 7/5 = 49/ 15 hours

(3) When the tube A is full, the tube B is evacuated.

49/ 15-4/3 = 29/ 15 hours

Xiao Ming walks from home to school in the morning. When he ran halfway, his father found that Xiao Ming's math book was left at home, and then he rode to deliver it to Xiao Ming. When he caught up, Xiao Ming still had 3/ 10 to go. Xiao Ming got on his father's car at once and was sent to school by his father, so Xiao Ming arrived at school five minutes earlier than walking alone. How long does it take Xiaoming to walk from home to school?

The speed ratio between dad riding a bike and Xiaoming walking is (1-3/10): (1/2-3/10) = 7: 2.

The time ratio between cycling and walking is 2: 7, so it takes 5 ÷ (7-2) × 7 = 7 minutes for Xiaoming to walk 3/ 10.

Therefore, it takes 7 ÷ 3/ 10 = 70/3 minutes for Xiao Ming to complete the race.

8. Car A and car B both start from place A and pass through place B to place C. The distance between the two places is equal to the distance from place B to place C. The speed of car B is 80% of that of car A. It is known that car B started earlier than car A 1 1 minute, but stayed in place B for 7 minutes, but car A drove all the way to place C. Finally, car B was later than car A..

There are more cars B than A, 1 1-7+4 = 8 minutes.

It takes 8 ÷ (1-80%) = 40 minutes to display dealership B, and 40× 80% = 32 minutes to display dealership A..

It takes 40 ÷ 2+7 = 27 minutes for the second car to stop at point B.

A train arrives at B in 32 ÷ 2+ 1 1 = 27 minutes after B train leaves.

That is, catch up with the b car in b place.

9. Two cleaning vehicles, A and B, perform road cleaning tasks between things. It takes 10 hour for car A to be cleaned alone, and 15 hour for car B to be cleaned alone. Two cars leave from east and west at the same time. When they met, car A was cleaner than car B12km. How many kilometers is it between East and West?

The speed ratio between car A and car B is 15: 10 = 3: 2.

When they met, the distance ratio between car A and car B was also 3: 2.

Therefore, the distance between the two cities is 12 ÷ (3-2) × (3+2) = 60km.

/kloc-4 containers of 0/0.3 tons, 5 containers of 2.5 tons, 1 0.5 tons/4 containers, and 7 containers of1ton. So how many cars with a load of 4.5 tons are needed to transport all the containers at once?

My solution is as follows: (* * 12 cars)

The point of this problem is that containers cannot be unpacked like other things. Therefore, we should consider the issue of distribution.

3 tons (4 cars) 2.5 tons (5 cars) 1.5 tons (14 cars) 1 ton (7 cars)

Four, four, four cars.

Two, two, two cars.

Six, six, three cars

2 1 1 vehicle

6 Respondents with two cars: 1085039267 | Level 1 | 2010-6-1910: 36.

First, fill in the blanks. (24 points)

1. At present, the total area of China and Hongkong is1052 million square meters, and the unit of "ten thousand" is rewritten as () square meters, and the mantissa after omitting "hundred million" is about () square meters.

2, 4.25 hours = () hours () minutes, 7 cubic meters and 40 cubic meters = () cubic meters.

3. Cut the 4-meter-long rope into 5 sections on average, each section is () meters, and each section accounts for () of the total length.

4.3 14%, 3. 1, 3.0 14, 3,3, the maximum number is (), and the minimum number is ().

5.()% = 4 ÷ 5 = (): 10 = () (decimal)

6. There are () simplest true fractions with denominator 18, and their sum is ().

7. Glue three cubes 4 cm long together to form a cuboid. The cuboid has a volume of () cubic centimeters, and its surface area is () square centimeters smaller than the original three small cubes.

8, more than 80 meters is () meters, 12 kg is 15 kg ()%.

9. The diagonal length of a square piece of paper is 4 cm, and its area is () square cm. If cut into the largest circle, the area of the circle is () square centimeters.

The ratio of 10 to: is (), and the ratio of 4: 0.8 to the simplest integer is (): ().

The greatest common factor of 1 1, 12 and 30 is (), and the smallest common multiple is ().

12, observe the law of finding examples and answer questions as required.

( 120× 120)-( 1 19× 12 1)= 1, ( 120× 120)-( 1 18× 122)=4,

( 120× 120)-( 1 17× 123)=9,( 120× 120)-( 1 16× 124)= 16,……

( 1)( 120× 120)-( 1 12× 128)= ()。

(2)( 120× 120)-( × )= 144

Second, the judgment question. (5 points)

1, add 0 or go to 0 after the decimal point, and the size of the decimal point remains the same. ( )

2. The volume of the cone is equal to the volume of the cylinder. ( )

3. One ton of coal is 40% used, leaving 60% tons. ( )

Time is fixed, and distance is directly proportional to speed. ( )

5. The price of a commodity first increases by 10% and then decreases by 10%. The current price of this commodity is the same as the original price. ()

Third, multiple choice questions. (6 points)

1, the divisor of two numbers is 2.4. The divisor is enlarged by 100 times, and the quotient is () if the divisor is divided by 0.0 1.

a、2.4 B、24000 C、240

2, said a patient's temperature changes in a day, draw () statistical chart is more appropriate.

A, dotted line b, sector c, bar

3, an isosceles triangle, the ratio of a base angle to a vertex angle is 2: 1, then this isosceles triangle is also ().

A, acute triangle b, right triangle c, obtuse triangle

Xiao Ming walked 20 kilometers in 3 hours, and rode back along the original road just 1 hour. The average speed of Xiao Ming's round trip is () per hour.

A, 5km b,10km c,13km.

5. A project was originally planned to be completed in 5 hours, but the task was actually completed in 4 hours, which improved the work efficiency ().

A, B, C,

6. When estimating 7. 18×5.89, the error is small ().

a、8×6 B、②7×6 C、③7×5

Fourth, the calculation problem. (26 points)

1. Numbers written directly (10 points)

127+38= 8.8÷0.2= 15×3/20= 2/3÷0.5÷2= 13/4+0.25=

2/5÷ 1/ 10= 2/3— 1/4= 2.8—4/7+ 1.2= 3.5×9+3.5= 1.02-0.43=

2. calculation. (12)

9 -(3 +0.4) 1.8× +2.2×25% 5.02- 1.37-2.63

3. Solve the equation. (4 points)

7.5:x=24: 12 3x-6 =8.25

Verb (abbreviation for verb) figure and operation. (8 points)

1, a part, as shown below, find its volume. (4 points)

2. The side length of each small square in the right square is 1 cm. Please draw this picture.

The trapezoid in the shape is divided into three triangles, A, B and C, so their area ratio is

1∶2∶3, and calculate the areas of the three triangles respectively. (4 points)

Sixth, solve the problem. (3 1)

1, only counting the column type, not counting: (2 points for each question, ***8 points)

(1) A factory plans to produce 240 machine tools in 15 days, but in fact, it produces 4 more than planned every day. How many days will it actually take to complete?

(2) The survival rate of a sapling is 95%. How many saplings must be planted at least to ensure 570 saplings?

(3) The store delivered 20 baskets of pears and 0/6 baskets of apples, weighing 820kg. It is known that each basket of apples weighs 22.5 kilograms. How many kilograms does each basket of pears weigh? (Equation solving)

(4) ICBC introduced lump-sum deposit and withdrawal of education savings, and implemented interest tax relief. Xiao Qiang's parents went to the bank to deposit 8,000 yuan as a three-year lump-sum education savings in Xiao Qiang. It is known that the annual interest rate of lump sum deposit and withdrawal for three years is 3.24%. How much principal and interest can I get at maturity?

2. Xiaoming reads a story book. In the first four days, he read an average of 24 pages a day, and on the fifth day he read 34 pages. How many pages did Xiao Ming read every day for the first five days? (4 points)

There is an 80-meter-long water pipe, which used 25% of the total length for the first time, 40% more than the first time. How many meters are left after two times? (4 points)

4. A cylindrical barrel without a lid, measured from the inside, has a bottom diameter of 4 decimeters and a height of 6 decimeters. How many square decimetres of iron sheet does it take to make this barrel? The water depth in the bucket is 5 decimeters. How heavy is the water in the bucket? (1 liter weight 1 kg) (5 points)

The distance between a and b is 264 kilometers. A takes a bus from A to B, with an average of 80 kilometers per hour. B rides a motorcycle from B to A with an average speed of 32 kilometers per hour. A travels 200 kilometers and meets B. How many hours does A have to leave before B? (5 points)

6. One day, Zunyi Evening News published a message: the monthly water fee for each household in a city was changed from per cubic meter 1.90 yuan to:

water consumption

20 cubic meters and below

More than 20 cubic meters

charging standards

2.30 yuan per cubic meter

3.5 yuan per cubic meter

According to the above information, the water fee of the Wangs in May this year was paid to 24 yuan more than before according to the new charging standard. How many cubic meters of water did the Wangs consume in May this year? (5 points) Agree with 5 comments.