Find the sixth grade math problem calculation problem application problem (need a lot of best exercises) and so on.

2. There is a triangle whose area is equal to the area of a circle with a diameter of1m. It is known that the base of the triangle is1.57 m. What is the height of the triangle?

3. Divide a circular piece of paper into several equal parts, cut it open and spell it into an approximate rectangle with the same width and radius. The circumference of this rectangle is 16.56 cm, so how many square centimeters is the area of this circular piece of paper?

There is a project, team A needs 20 days, team B needs 24 days, and team C needs 30 days to complete it alone. Now the three teams are working together, but Team A was evacuated to another construction site halfway, and it took 12 days to complete the project. When Team A retreats, how many days will it take for the epidemic teams to work together?

1. Chickens and rabbits live in the same cage. * * * There are 100 heads and 280 feet. How many chickens and rabbits are there?

2. Chickens and rabbits live in the same cage, * * * has 168 feet, and rabbits have more 12 than chickens. How many chickens and rabbits are there?

3. Dong Zhang bought 38 stamps from 2 yuan and 5 yuan, and spent a total of 106 yuan. How many stamps did you buy each?

4.60 Students went boating and just took 1 1, including 6 people in the big boat and 4 people in the small boat. How many big boats and small boats are there?

5. There are 20 questions in a quiz. If you do one question correctly, you will get 6 points, and if you do one wrong, you will get 3 points. Xiao Huan answered all the questions and got only 70 points. He answered several questions correctly.

In a rectangular container, there is water with a depth of 12 cm. Due to the sudden change of weather, there was a layer of ice on it, and the thickness of ice was 3.6 cm. It is known that the volume of water turned into ice has increased by 1 1. What is the water depth under the ice?

(1) In Xiaoyang's final exam, the average score of Chinese and mathematics was 96, and mathematics was 8 points more than Chinese. Chinese is () points, mathematics is () points.

(2) Warehouse A and Warehouse B have 42 tons of rice. If 3 tons of rice is transferred from warehouse A to warehouse B, the amount of rice in the two warehouses is exactly the same. It turns out that warehouse A stores () tons of rice and warehouse B stores () tons of rice.

(3) The combined age of father and grandfather 1994 is 127 years old. Grandpa was 37 years older than his father ten years ago and was born in ().

(4) There is a parking lot with 24 cars, including 4 wheels for cars and 3 wheels for motorcycles. These cars have 86 wheels. There are () motorcycles among them.

(5) The number of students participating in the Children's Palace Science and Technology Group is 35 less than last year, which is 4 1 person less than last year. There are () students participating in the science and technology group this year.

(6) The father is 47 years old and the son 19 years old. Years ago, my father was five times as old as my son.

(7) A tree planting group plants trees. If each person plants 5 trees, there are 14 trees left; If there are seven trees for each race, there will be four fewer trees. There are () people in this tree planting group, and one of them can plant () trees.

2. The sum of A, B and C is 1 160, A is half of B and B is twice of C ... What are these three numbers?

3. A guest house has a meeting, and there are 3 people in each room, so 36 people have no beds; If there are 4 people in each room, there are 13 people who have no beds. What will happen if there are five people living in each room?

4. Xiaoming reads a book, with 83 pages on the first day, 74 pages on the second day, 7 1 page on the third day and 64 pages on the fourth day. The number of pages read on the fifth day is 3.2 pages more than the average number of pages read in these five days. How many pages did Xiao Ming read on the fifth day?

5. Measure the height of the bridge on the bridge. When the rope is folded in half and hung to the water surface, there are 8 meters left in the rope; After the rope was folded three times, it was still 2 meters above the water. Find the height of bridge and the length of rope.

6.44 Students rowed and took a boat 1 * * *, including 6 people in the big boat and 4 people in the small boat. How many big boats and small boats are there?

7. In the fourth grade of the experimental primary school, a math contest was held, and one * * * gave 10 questions. If you answered one question correctly, you will get 10 points, and if you answered one question incorrectly, you will be deducted 5 points. Zhang Hua finished all the 10 questions and got 70 points. He answered several questions correctly.

8. Buy 4 pencils and 5 erasers and send them to 6 yuan; Buy the same 6 pencils and 2 erasers, 4.60 yuan. How much is each pencil and eraser?

9. Build a road. Half of it was built on the first day, with a total length of more than 6 meters. The next day, the remaining half was built less than 20 meters. On the third day, 30 meters were built. Finally, 14 meter is left. How long is this road?

10. Zhang Qiang bought a coat, a hat and a pair of shoes with 270 yuan. Coat is more expensive than shoes 140 yuan, coat and shoes are more expensive than hats 2 10 yuan. How much did Zhang Qiang spend on this pair of shoes?

1 1. The Hong Guang factory plans to produce 40 refrigerators every day. After technological innovation, five more refrigerators will be produced every day than originally planned, thus completing this batch of production tasks two days ahead of schedule and producing 35 more refrigerators than originally planned. How many refrigerators have actually been produced?

12. Professor 16, some with 1 graduate students, some with 2 graduate students, and some with 3 graduate students. They * * * brought 27 graduate students, of whom 1 graduate students have as many professors as there are two and three graduate students. How many professors are there?

4/9×3= 5÷ 1/3 = 1/2÷ 1/3 =

2 1/25÷42= 4/5×3/4 = 8.7×0.2=

4×0.25= 1/7× 14= 2/3÷5/6=

1.25×8= 3/5÷5/8= 6/7×3/2=

6×8.8= 4/ 1 1÷4= 4/9×3/8=

5/3÷5= 0÷8/3= 4/7-2/3=

2/7×2= 4 1/ 12×4= 4÷3/ 16=

12÷9/4= 75/8 ÷5= 12× 16/9=

2/3×3= 8÷9/4 = 5/3÷3/5 =

4/5×5/8= 7/9×9/7= 2.64+3.6=

2.4×50= 3500÷70= 2050-298=

2+7÷9= 0.3÷3%= 286+ 198=

3 14-202= 526+30 1= 223-99=

1/2×3/5= 1.89÷ 100= 0.82+0.08=

73× 1= 0.63× 10= 4÷ 10=

17÷ 1000= 0.56+0.4= 1.25× 100=

5.6+99= 43×63/2 1= 100÷25=

1-0.93= 90-0.9= 18.3× 1/3=

794- 198= 68×25= 43.3-63/2 1 =

72× 125= 300 1- 1998= 23/5×5/6 =

20/3× 12= 1/2- 1/6= 30.25×4/5=

5/6- 1/2= 1/2× 1/5=

4.25×4/25×4

57.26-(5.26- 1.5)

106.25+3.85-2. 125+3.875

1 1.9-2456×2 1

5/ 1 1-4×2.75

13.375+5.75+2.25+6.625

( 15. 1-9036)÷ 18

163.8×5.25+ 14.5

172. 1×4.3+5.7×2. 1

19. 102×45-328

2.8×3. 1+ 16/8

23÷(50- 12.5) ÷2.5

24×2/5× 1/3

25.6÷ 1 10×47+639

3.5×2.7-52.2/ 18

28- 1/7× 1/5

3.375×0.97+0.97×6.625

6.54+2.4+3.46+0.6

95.6× 1.8+95.6×8.2

35.6-420/ 12×4

344/3.6-5.4×0.25

16/2+30/2+90/6

5000- 105×34

0. 15/0.25+0.75× 1.2

4 1×( 1/2+ 1/3+ 1/4)×0.24

42×(25+4)×4

3×63/2 1-84

0.8 1/0.25+5.96×5

403÷ 13×27

46. 1.5×4.2-0.75÷0.25

3.27×4 +3.27×5.7

( 1.2+ 1.8)×4.5 1025-768÷32

0.25×80-0.45÷0.9

50. 1025-768÷32

8 1.2- 1 1÷7-×3=

6696÷62-6.5× 10.6 =

2/7×3/9 ÷2/7 =

6756- 193-207=

97×360+3×360=

4/9×3= 5÷ 1/3 = 1/2÷ 1/3 = 2/7×3/9 ÷2/7 = 2 1/25÷42= 4/5×3/4 = 8.7×0.2= 4×0.25= 1/7× 14= 2/3÷5/6= / kloc-0/.25×8= 3/5÷5/ 8= 6/7×3/2= 6×8.8= 4/ 1 1÷4= 4/9×3/8= 5/3÷5= 0÷8/3= 4/7 -2/3= 2/7×2 = 4 1/ 12×4= 4÷3/ 16= / kloc-0/2÷9/4 = 75/ 8 ÷5= 12× 16/9 = 2/3×3= 8÷9/4 = 5/3÷3/5 = 4/5×5/8 = 7/9×9/ 7 = 2.64+3.6= 2.4×50= 3500÷70= 2050-298= 2+7÷9= 0.3÷3%= 8 1.2- 1 1÷7-×3= 6696÷62-6.5× 10.6 =

1 125-997 998+ 1246+9989 (8700+870+87)÷87

125×8.8 1.3+4.25+3.7+3.75 17. 15-(3.5-2.85)

3.4×99+3.4 4.8× 1.0 1 0.4×(2.5÷73)

( 1.6+ 1.6+ 1.6+ 1.6)×25 ( + - )÷

12.3-2.45-5.7-4.55 2 + 0. 125×0.25×64

64.2×87+0.642× 1300 78×36+7.8×74 1-7 17+ 8

0. 125× +0.5 2.42 +4.58 -43

25÷ 100 4.25-3 -(2 - 1 )

( 1) 1.25* 17.6+36. 1/0.8+2.36* 12.5

1.25* 17.6+36. 1/0.8+2.36* 12.5

=(5/4)* 17.6+36. 1*(5/4)+23.6*(50/4)

= 176/8+36 1/8+236/8

=773/8=96.625

(2)7.5*2.3+ 1.9*2.5

7.5*2.3+ 1.9*2.5

=7.5*( 1.9+0.4)+ 1.9*2.5

=(7.5+2.5)* 1.9+7.5*0.4

= 19+3 =22

(3)2004/2003*2005

2004/2003*2005

=(2004/2003)*(2003+2)

=2004+4008/2003

(4)276*543-267/276+543*275

276*543-267/276+543*275

=543*(276+275)-267/276

=543*55 1-267/276

1. 125*3+ 125*5+25*3+25

2.9999*3+ 10 1* 1 1*( 10 1-92)

3.(23/4-3/4)*(3*6+2)

4.3/7 × 49/9 - 4/3

5.8/9 × 15/36 + 1/27

6. 12× 5/6 – 2/9 ×3

7.8× 5/4 + 1/4

8.6÷ 3/8 – 3/8 ÷6

9.4/7 × 5/9 + 3/7 × 5/9

10.5/2 -( 3/2 + 4/5 )

1 1.7/8 + ( 1/8 + 1/9 )

12.9 × 5/6 + 5/6

13.3/4 × 8/9 - 1/3

14.7 × 5/49 + 3/ 14

15.6 ×( 1/2 + 2/3 )

16.8 × 4/5 + 8 × 1 1/5

17.3 1 × 5/6 – 5/6

18.9/7 - ( 2/7 – 10/2 1 )

19.5/9 × 18 – 14 × 2/7

20.4/5 × 25/ 16 + 2/3 × 3/4

2 1. 14 × 8/7 – 5/6 × 12/ 15

22. 17/32 – 3/4 × 9/24

23.3 × 2/9 + 1/3

24.5/7 × 3/25 + 3/7

25.3/ 14 ×× 2/3 + 1/6

26. 1/5 × 2/3 + 5/6

27.9/22 + 1/ 1 1 ÷ 1/2

28.5/3 × 1 1/5 + 4/3

29.45 × 2/3 + 1/3 × 15

30.7/ 19 + 12/ 19 × 5/6

3 1. 1/4 + 3/4 ÷ 2/3

32.8/7 × 2 1/ 16 + 1/2

33. 10 1 × 1/5 – 1/5 × 2 1

34.50+ 160÷40

35. 120- 144÷ 18+35

36.347+45×2-4 160÷52

37(58+37)÷(64-9×5)

38.95÷(64-45)

39. 178- 145÷5×6+42

40.8 12-700÷(9+3 1× 1 1)

4 1.85+ 14×( 14+208÷26)

43. 120-36×4÷ 18+35

44.(58+37)÷(64-9×5)

45.(6.8-6.8×0.55)÷8.5

46.0. 12× 4.8÷0. 12×4.8

47.(3.2× 1.5+2.5)÷ 1.6

48.6- 1.6÷4= 5.38+7.85-5.37=

49.7.2÷0.8- 1.2×5= 6- 1. 19×3-0.43=

50.6.5×(4.8- 1.2×4)=

5 1.5.8×(3.87-0. 13)+4.2×3.74

52.32.52-(6+9.728÷3.2)×2.5

53.[(7. 1-5.6)×0.9- 1. 15] ÷2.5

54.5.4÷[2.6×(3.7-2.9)+0.62]

55. 12×6÷( 12-7.2)-6

56. 12×6÷7.2-6

57.0.68× 1.9+0.32× 1.9

58.58+370)÷(64-45)

59.420+580-64×2 1÷28

60. 136+6×(65-345÷23)

15- 10.75×0.4-5.7

62. 18. 1+(3-0.299÷0.23)× 1

63.(6.8-6.8×0.55)÷8.5

64.0. 12× 4.8÷0. 12×4.8

65.(3.2× 1.5+2.5)

1, 2005 is the 600th anniversary of China's great navigator Zheng He's voyage to the Western Ocean, and the Spanish great navigator groome Bu's first voyage to the Western Ocean was in 1492. How many years is the difference between these two ocean voyages?

2. Starting from the date of winter solstice, it is divided into a section every nine days, which is called September 19, February 29, ..., followed by September 9. The winter solstice in 2004 was 65438+February 2 1, and February 4 in beginning of spring in 2005. When is the beginning of spring?

3. On the lower right is the surface development diagram of a straight triangular prism, and the yellow and green parts are squares with side length equal to 1. What is the volume of this triangular prism?

My father, mother, guests and I are drinking tea around the round table. If we only consider the situation of everyone's neighbors, how many different sitting methods are there?

5. In Olympic triathlon, the distance of bicycle is four times that of long-distance running, the distance of swimming is 3/80 of that of bicycle, and the difference between long-distance running and swimming is 8.5 kilometers. Find the total distance of three terms.

6. As shown on the right, use regular triangles of the same size to splice the larger regular triangles one by one. The number of minimum triangle vertices (overlapping vertices are only calculated once) is as follows:

3, 6,10,15, 21,... What is the ninth column?

7. A conical container A and a hemispherical container B, the diameter of their circular openings and the height of the container are shown in the figure. If container A is used to fill container B with water, how many times should it be filled at least?

8. 100 students participated in social practice, including 2 senior students, 3 junior students and 4 1 group. Q: How many students are there in the senior and junior grades?

Xiaoming bought some exercise books at retail price with 48 yuan money. If you buy it at the wholesale price, it's 2 yuan cheaper per copy, so just buy four more copies. Q: What is the retail price of each book?

10 and students younger than 100 have two combinations when dancing in group dance: one is the middle group with 5 people and the others are surrounded by 8 people; The other is a group of 8 people in the middle and a group of 5 others. How many students are there at most?

1 1, infusion 100 ml, 2.5 ml per minute. Please observe the data in the bottle image at 12 minutes and answer the question: What is the volume of the whole bottle?

12. The acute angle or right angle formed by the intersection of two straight lines is called the "included angle" of the two straight lines. There are several straight lines crossing each other on the current plane, and the "included angle" can only be 30, 60 or 90. Q: How many straight lines are there at most?

the second part

1. Only one of the four options in each of the following multiple-choice questions is correct. Please write the English letters indicating the correct answers in brackets after each question. (6 points for each small question)

Of the six figures composed of 1. jigsaw puzzle, () have symmetry axes.

(regardless of splicing line)

5 (B) 2 (C)3 (D)4

2. There are four propositions as follows:

① The maximum negative number is-1; ② The smallest integer is1;

③ The maximum negative integer is-1; ④ The minimum positive integer is1;

There are () true propositions among them.

1 (B)2 (C)3 (D)4。

3. If a, b and c are all positive numbers, A (b+c) = 152, B (c+a) = 162 and C (a+b) = 170, then the value of abc is ().

672 (B)688 (C)720 (D)750

4. The following figure shows the front view, left view and right view of 3D graphics in centimeters. The volume of a three-dimensional figure is () cubic centimeters.

(A)2 (B)2.5 (C)3 (D)3.5

5. The speed of ships A and B sailing in still water is v 1, v2, (V 1 > V2) respectively, and the channel distance between downstream port A and upstream port B is 150km. If ship A sails from port A and ship B sails in the opposite direction at the same time, the two ships meet at point C on the way. If ship B sets sail from port A and ship A sets sail from port B at the same time, and the two ships meet at point D on the way, it is known that the channel distance between C and D is 2 1 km. Then v 1∶v2 is equal to ().

(A) (B) (C) (D)

6. There is a string of numbers: 1, 22, 33, 44, ..., 20042004, 20052005, 20062006. Daming calculates the sum of the last digits of the previous 1003 numbers from left to right, and records it as a; Xiaoguang calculates the sum of the last few digits of the remaining 1003 number, and records it as B, so A-B = ().

(A)-3(B)-3(C)-5(D)5

Two. Group A fills in the blanks (8 points for each small question)

7. Draw a large semicircle with AB as the diameter, as shown in the figure. BC=2AC

Draw two small semicircles in the big semicircle, with AC and CB as diameters respectively.

Then the ratio of shadow area to semicircle area is equal to _ _ _ _.

8. Calculation:

( 1+ ) ( 1+ ) ( 1+ ) ( 1+ ) … ( 1+ ) ( 1+ )=__

9. Gas station A and store B are on the same side of the road MN, and the distance from A to MN is greater than B.

The distance to MN is AB = 7m, and the pedestrian P walks on the road MN.

Q: When the difference between the distance from P to A and the distance from P to B is the largest,

This difference is equal to _ _ _ _ meters.

10, if =42, then x+y = _ _ _ _ _ _

Three. Group B fills in the blanks (two blanks for each question, 4 points for each blank)

1 1. After the train speeds up, a train leaves from City A at 2 1: 00 and arrives at City B at 7: 00 the next day. The running time is 2 hours shorter than before the speed increase, but the speed is 20 km/h faster than before the speed increase, so the average speed before the speed increase is km/h, and the two cities are several kilometers apart.

12, the formula is in progress.

Eleventh session

+China Cup Competition

2 0 0 6

In Chinese, the Chinese characters "first, tenth, first, sixth, middle, cup and match" represent nine numbers in 1 ~ 9, and different Chinese characters represent different numbers, which just makes the addition formula valid. Then there are different filling methods * * *; The maximum possible value of the three-digit China Cup is.

13. Among the monomials composed of x, y and z, choose the monomials that meet the following conditions:

1) coefficient is1;

2) The sum of powers of x, y and z is less than or equal to 5;

3) exchange the powers of x and z, and the single item remains unchanged.

Then you can pick out such a monomial. In the selected monomials, multiply the lowest power of x by pairwise to get a set of monomials, and add these groups of monomials (similar items should be merged) to get an algebraic expression, so the algebraic expression is the sum of different monomials.

14. There is a square in the picture below.

There is a triangle.

the third part

1, 1999 How many ways are there to divide the sum of two prime numbers?

2. Macao has a population of 430,000, 90% of which live on a peninsula with an area of 7 square kilometers. What is the average population of the peninsula per square kilometer? (Take two decimal places)

Someone bought a stock last year, and it fell by 20% that year. It should be increased by several percentage points this year to maintain the original value.

Yin Hua Building has seven floors, and the red light on each floor is doubled. There is a red light of 38 1 in the * *. How many red lights are there on the fourth floor?

6. The figure on the left is a figure composed of nine equilateral triangles. It is known that the side length of the smallest equilateral triangle in the middle is 1. What is the circumference of this hexagon?

7. A regular hexagonal nursery is divided into many equal regular triangles by a straight line parallel to the edge of the nursery, and seedlings are planted on the vertices of the triangles. It is understood that 90 saplings have been planted in the outermost circle of the nursery. How many saplings are planted in the nursery?

8. The total number of primary school students in A, B and C is 1999, which is known to be twice that of A, B minus 3, C plus 4 .. What are the students in A, B and C schools?

9. Grandpa Xiaoming's age is double digits. The number obtained by exchanging these two digits is Xiao Ming's father's age. The age difference between them is four times that of Xiao Ming. What's Xiaoming's age?

10. Make a cuboid with a length of 7 cm, a width of 5 cm and a height of 3 cm with 10 cuboid building blocks. What is the minimum surface area of this cuboid?

1 1. The hour hand and minute hand of the clock are reversed into a straight line at 6 o'clock. When is the next reversal into a straight line? (accurate to the second)

part four

First, the calculation problem

1. If is, the value of.

2. Known, the value of.

3. The two known sums are both natural numbers. Find the minimum value of.

4. Known, find the value of the algebraic expression.

5. It is known to be an integer greater than 1, and the trial judgment is (odd/even/multiple of 4). (Choose the correct answer from the brackets)

6. There are no more than 50 students in Class A, Grade 6 in a school. Once in an exam, some students got an A, some students got a B, some students got a C, and the rest failed. How many students are there in this class?

7. Give a group of children 50 candies, each child has at least one candy, and everyone gets a different number of candies.

How many children are there at most?

8. How many triangles are there in the diagram 1?

9. As shown in Figure 2, it is an equilateral triangle. The sum of quadrilaterals is a square, so find.

10. Change the position of each number in the five-digit 24678 at will. How many prime numbers do you get?

1 1. Try to reduce it to the simplest band score.

12. The famous Goldbach conjecture is that any even number greater than 7 must be represented by the sum of two different prime numbers.

Let's go For example, 18 can be written as "5+ 13" or "7+ 1 1". Representing even numbers with Goldbach conjecture

126, find the smallest product between two prime numbers.

Second, the application problem (need to write the main steps)

13. After eight o'clock, when did the hour hand and the minute hand first coincide? The answer is accurate to the point.

14. Figure 3 shows a circle and two semicircles with diameters of and respectively. Given a line with three centers, find the area ratio of the shadow part to the blank part.

15. Two cars travel from place A to place B at the same time. As we all know, a car travels half a distance at a speed of 80 km/h, and then it takes time.

Drive the remaining half distance at the speed of 100km/h; And car B travels at a speed of 80km/h half the time.

Drive, and drive at the speed of 100km/h/h for the other half of the time. Which bus gets to B first?

16. Write the numbers from 0 to 9 repeatedly in the order of 1, 2, 3, …, 9, 0, 1, 2, 3… to form one.

A 2006-bit natural number. Try to determine whether this number is divisible by 6.

17. A box of candy does not exceed 200 pieces. If sugar is taken out in the form of 2, 3, 4 or 6 grains respectively, there is always 1 grain left in the box; But every time the sugar is taken out in the form of 1 1, and it's over. How many sweets are there in the box?

The fifth part

First, the calculation problem (1- 12) does not need to write steps, just fill in the answers.

1. Calculation:.

2. What you know, what you pursue.

3. If it is a natural number, and what is the minimum number that can be obtained?

4. It is known that no matter what value X takes, the score must be the same constant value to get the value.

5. It is known that m is odd, n is even, and the equation.

All the solutions are integers, so judge the parity of integers p and q.

6. If the convex polygon has only one internal angle, the sum of other internal angles is 20000. Try to find the value of. Figure 1 shows a regular octagon. It is known that △ABC in the figure is an equilateral triangle, so ∠DCE is found.

8. Figure 2 shows a large square consisting of 25 small squares. If * * * can be counted in the picture.

The value of.

9. As we all know:

, and none of them are equal to 0. Find all possible values.

10. If it is the solution of inequality, find the minimum integer value of.

1 1. At a party, * * * 10 couples attended. If every man shakes hands with others except his spouse, women don't have to shake hands with women. How many times did the guests shake hands at the party?

12. What is the maximum value of the quotient obtained by dividing a two-digit number by its sum?

Second, the solution (13-20) This part must list the calculation process and answers on the answer sheet.

13. If,

The value.