1. An adult breathes 16 times per minute, inhaling 500 cubic centimeters of air each time. Q: How many cubic meters of air does he breathe in a day and a night?

2. The following is a multiplication formula: Q: What is the sum of four numbers when the product is maximum?

3. An 84-episode TV series, which starts on a Sunday, broadcasts 1 episode every day from Monday to Friday and stops broadcasting on Saturday. Q: When was the last episode aired?

4. Calculation:

5. Use four cards with numbers written on them to form four numbers. Q: What is the sum of the minimum number and the maximum number?

6.a and B swam from the same place at the same speed and direction in the river. Now a is in front of b, and b is 20 meters away from the starting point; When B swims to where A is now, A is 98 meters away from the starting point. Q: How many meters is A from the starting point now?

7. There are 4 coins with face value 1 minute, 2 cents and 5 cents, which are used to pay 23 cents. Q: How many different payment methods are there?

8. There are two cylindrical glasses, A and B, whose inner diameters are 10 cm and 20 cm respectively, and there is a proper amount of water in the glasses. An iron block sank into glass A. When the iron block was taken out, the water level in glass A dropped by 2 cm. Then sink the iron into the second cup, and the water in the second cup does not overflow. Q: How many centimeters did the water level in the second cup rise at this time?

9. Three students, A, B and C, went out for lunch, and * * * bought 1 kg and four steamed buns. Party A had no money, and Party B and Party C paid for 8 and 6 buns respectively. Party A ate as much as Party B, and Party C ate/kloc-0 buns more than Party B. The next day, Party A brought his 2 yuan score of 30.4. Q: Yes.

10. As shown in the figure below, the curves in the figure are connected by six semicircular curves with the ratio of radius to length of 2: 1.5: 0.5. Q: What is the area ratio of the shadow part to the non-shadow part?

1 1. Xiaoming's age this year is the sum of the figures in the year when he was born. Q: How old is he this year?

12. The picture below is a garden plan, in which the square is the grass; Round is bamboo forest; The area of bamboo forest is 450 square meters more than that of grassland. Q: How many square meters is this swimming pool?

13.50 students stand in a row facing the teacher, and count off from left to right according to the teacher's password: 1, 2, 3, ..... After the report, the teacher asks the students who reported 4 times to turn back, and then the students who reported 6 times to turn back. Q: How many students are still facing the teacher?

14. As shown in the figure below, the big circle covers half of the area of the small circle. Q: Which is longer, the arc AmB of the big circle or the diameter of the small circle?

15. For the two digits 10,1,…, 98, 99, a decimal point is added between the digits of each number divided by 7 and the decimal digits, and the other numbers remain unchanged. Q: What is the sum of all the figures after this change?

16. Some people work continuously for 24 days, earning 190 yuan (daily wage 10 yuan, half-time job on Saturday, rest on Sunday, no pay). It is known that his work started on the day in late October of 1 year 1 month, and this month's1happens to be a Sunday. Ask.

1. 1 1.52 m3 2.24 3. The last episode is on Friday at 4. The original formula is equal to 3.55.115176.59 meters.

7. Five kinds of 8.0.5 cm 9. 0.36 yuan10.1.21year 12. 150m2 13. 38.

14. The arc of the great circle is longer15.36438+06.416.218.

1. One night is 60× 24 = 1440 minutes.

The air intake of an adult is 500×16×1440 =11520000 (cubic centimeter), which is 1 1.52 cubic meters.

2. The product of solution is a double digit, which is a multiple of 5, so the maximum is 95.95 ÷ 5 = 19, so the formula in the problem is actually

So the sum of four numbers is 1+9+9+5 = 24.

3. Six episodes are broadcast every week, 84 episodes are broadcast for 84 ÷ 6 = 14 weeks, and the first episode is broadcast on Sunday, so the last episode is broadcast on Friday.

4. Solve the original formula =

=

=

5. The maximum number of solutions is 995 1 and the minimum number is 1566. So the total is 9951+1566 =1517.

6. Solution When B swims to A's current position, A swims the same distance, that is, (98-20) ÷ 2 = 39 (meters), so A is now 39+20 = 59 (meters) from the starting point.

7. You must pay 23 cents for the solution. You can only use four nickels at most. Because 1 cent and 2 cents are used, the value of * * is 12 cent, so at least three nickels should be used. When using three nickels, 5× 3 = 15, 23- 15 = 8, so use at most four nickels and at least two nickels.

23= 15+(2+2+2+2),

23 = 15 decimal (2+2+2 decimal 1+ 1).

23 =15+(2+2+1+1), three payment methods.

When four nickels are used, 5× 4 = 20, 23-20 = 3. So the maximum usage of 2 cents is 1 block, so you can have

23=20+(2+ 1)

23 = 20+(1+1+1), so * * * has five different payment methods.

8. If the ratio of the diameters of two cylinders is 1: 2, then the ratio of the bottom surface area is 1: 4, and the volume of water displaced by iron blocks in two cups is the same, then the height of water rising in the second cup should be the height of water falling in the first cup, that is, 2×= 0.5(cm).

9. Take off the armor (14- 1) ÷ 3 = (two), every two 234 ÷ = 54 (points),

The value of c is 54× (6- 1-) = 36 (points).

Answer: c 0.36 yuan should be paid.

10. Let 1 be the radius of the smallest semicircle. Then the radii of the other two semicircles are 3 and 4, respectively, representing the areas of the shaded part and the non-shaded part.

=π× + ×π× + ×(π× -π× )=5π,

=π× - = 1 1π,

therefore

A: The ratio sought is.

1 1. Suppose Xiaoming was born in, then1+9+A+B = 95-10A-B.

So 1 1A+2B = 85.

When a≥8,11+2b > 85; When a≤6,1/a+2b ≤ 66+2× 9 = 84, so there must be a = 7 and b = 4. Xiaoming 1+9+7+4 = 2 1 this year.

12. Let's take the pool area as 1 unit. Then the area of grassland is 3 units, and the area of bamboo forest is 6 units. Therefore, the area of bamboo forest is (6-3 =) 3 units. The area of three units is 450 square meters, so the area of 1 unit is 450 ÷ 3 = 650.

A: The swimming pool covers an area of 150 square meters.

13. Solution Because 50 ÷ 4 = 12 … was on 2, it was the first time that students with 12 turned back; And 50 ÷ 6 = 8 … is greater than 2, so the second time, eight students made a backward turn. Among them, the students who reported multiples of 4 and 6 at the same time turned their backs to the teacher for the first time, and then turned back. These students faced the teacher again. The least common multiple of 4 and 6 is 12, so the number of people who turn back twice is 4. (Because 50 ÷12 = 4 ... 2)

So there are still 50- 12-(8-4)+4 = 38 (name) still facing the teacher.

14. Solution First, the center of a small circle must be in the overlapping area of two circles. Otherwise, as can be seen from the picture on the left below, the part covered by the big circle is less than half of the area of the small circle.

Let A and B be the intersection of two circles, 0 is the center of a small circle, 0 connects OA and OB with a big arc on the same side of the chord AB, and C+CB = AO+OC+CB > OA = Ob = the diameter of the small circle, and the arc of the big circle > AC+CB, so it is greater than the diameter of the small circle.

15. The sum of the original solutions is

10+ 1 1+…+98+99= =4905

The two digits divided by 7,2 are 7× 2+2 = 16, 7× 3+2 = 23, …, 7× 13+2 = 93.

*** 12 number. After adding decimal points to these numbers as required in the question, they all become original numbers, so this program reduces the total.

( 16+23+…+93)×( 1- )= × =588.6

Therefore, after the change, the sum of all figures is 4905-588.6 = 43 16.4.

16. The solution is 3× 7 < 24 < 4× 7.

So the number of saturdays and sundays in 24 days. It can only be 3 or 4, and 190 is an integer multiple of 10. So the number of Saturday days in 24 days is even, so it is 240- 190 = 50 (yuan).

We can know that there are exactly four Saturdays and three Sundays in these 24 days. Sunday is always immediately after Saturday. Therefore, the day when this person finishes his work must be Saturday. We can know that the start date is Thursday, because .65438+1 October1is Sunday, so 65438+1October 22nd is also Sunday, so the only Thursday in the last ten days of 65438+1October 26th is 65438+/kloc. Back from 65438+1October 26th, we can know that the 24th day is February 10.

Examination questions and answers of the fifth China Cup rematch.

Calculation:

Two students, A and B, originally planned to study by themselves at the same time every day. If A increases the self-study time by half an hour every day and B decreases the self-study time by half an hour every day, then the six-day self-study time of B is only equivalent to A's 1 day .. Q: What was the original self-study time of Party A and Party B?

3. Figure 5-4 consists of a circle, a semicircle and a straight line segment. Try to calculate the area of the whole "pig" (accurate to 1mm2) except the shaded part in the figure by measurement.

4. When the sheep and the wolf are together, the wolf will eat the sheep, so we have stipulated an operation about the sheep and the wolf, using the symbol △:

Sheep △ sheep = sheep; Sheep △ Wolf = Wolf; Wolf △ sheep = wolf; Wolf △ Wolf = Wolf

The above calculation means: sheep and sheep are still sheep, wolves and wolves are still wolves, but wolves and sheep are just wolves.

Children always hope that sheep can beat wolves, so we have stipulated another operation, using the symbol ☆:

Sheep ☆ sheep = sheep; Sheep ☆ Wolf = sheep; Wolf ☆ sheep = sheep; Wolf = Wolf.

This operation means: sheep and sheep are still sheep, wolves and wolves are still wolves, but because sheep can beat wolves, when wolves and sheep are together, they are driven away by sheep, leaving only sheep.

For sheep or wolves, you can use the above operations for mixing operations. The rule of mixed operation is from left to right, and the result of operation is either sheep or wolf.

Find the following results: sheep △ (wolf ☆ sheep) ☆ sheep △ (wolf △ wolf)

Human blood is usually type A, B, O and AB. The relationship between children's blood types and their parents' blood types is shown in the following table:

Parents' blood type, children's possible blood type

Oh, oh

Oh, oh, oh.

Oh, oh, oh.

o，AB A，B

Ah, ah, ah, ah.

A，B A，B，AB，O

A，AB A，B，AB

B，B，B，O

AB A，B，AB

AB，AB A，B，AB

At present, there are three children wearing red, yellow and blue coats, and their blood types are O, A and B in turn. Every child's parents wear hats of the same color, including dividend, yellow and blue, which in turn indicate that their blood types are AB, A and O. Q: What color hats do parents of children wearing red, yellow and blue coats wear?

6. A balance, with several white balls of equal weight on the right panel and several black balls of equal weight on the left panel. Both sides are balanced at this time. Take a white ball from the right plate and put it in the left plate, then take two black balls from the left plate and put them in the right plate, and add 20 grams of brick yards to the left plate at the same time. At this time, the two sides are also balanced, such as moving two white balls from the right disk to the left disk and moving a black ball from the left disk to the right disk. Q: How many grams do the white ball and the black ball weigh?

7. A pool full of water, with a water inlet valve and three drainage valves with the same caliber. If the inlet valve and the drain valve are opened at the same time, the water in the pool can be drained within 30 minutes; If the inlet valve and the two drain valves are opened at the same time, 10 minutes can drain the water in the pool. Q: How many minutes does it take to close the inlet valve and open three drain valves at the same time to drain the water in the pool?

8. How many different ways are there to divide 37 by the sum of several different prime numbers? Multiply the prime numbers removed in each method, which product is the smallest?

9. There are only uphill roads and downhill roads from A to B, and there is no smooth road. The speed of the car is 20 kilometers per hour when going uphill and 35 kilometers per hour when going downhill. It takes 9 hours to drive from A to B and 9 hours to drive from B to A. Q: How many kilometers is the road between A and B? How many kilometers do I have to walk uphill from A to B?

10. Fill in a number in each cell without a number in the figure below, so that the sum of three numbers in each row, column and diagonal is equal to 19.95. Then, draw "?" What are the numbers in the box?

1 1. A cylindrical container filled with water, with a bottom radius of 5cm, a depth of 20cm and a water depth of 15cm. Now put an iron cylinder with a bottom radius of 2cm and a height of 17cm vertically into the container. What is the depth of the container at this time?

12. Three identical cups numbered 1, 2, 3 were filled with half a glass of water respectively. Cup 1 contains100g sugar, and Cup 3 contains100g salt. First, pour half of the liquid in the 1 cup and the liquid in the No.3 cup.

What is the integer part of 13?

14. A large rectangle with a circumference of 56 cm is divided into four small rectangles, as shown in (a) and (b) in Figure 5-5. In (a), the area ratios of small rectangles are a: b = 1: 2, and b: c = 1: 2. The corresponding ratios in (b) are: = 1: 3,: = 1: 3, and the ratio of the difference obtained by subtracting the width of d from the width of a known rectangle to the difference obtained by subtracting the length is 1: 3. Find the area of a big rectangle.

15. At the speed of 160km per hour, a car and b car leave at the same time, at the same place and in the same direction on the 2 10km long circular highway. Whenever car A catches up with car B, car A slows down and car B accelerates. Q: How many kilometers did the two cars travel at exactly the same speed?

16. try to explain that when sum is written as the simplest fraction m/n, m will not be a multiple of 5.

17. At present, there are 1 1 pieces of iron, and the weight of each piece is an integer. Any 10 block can be divided into two groups with equal weight, each with 5 pieces of iron. Please explain that the weight of this 1 1 piece of iron is equal.

1. The original formula is equal to. I originally planned to study for 42 minutes every day. 3.≈ 1093 mm2. 4. Sheep △ (Wolf ☆ Sheep) ☆ Sheep △ (Wolf △ Wolf) = Wolf 5. Parents of children in red shirts wear blue hats; Parents of children in yellow coats wear yellow hats; The parents of the child in the blue coat are wearing red hats. 6. Each black ball weighs 15g, and each white ball weighs 20g. 7. It will take 5 minutes. 8.* * * 10 Different demolition methods, of which 9 are the smallest. The length of the road between Party A and Party B is 2 10km. From A to B, you need to take the uphill road of 140km, 10. The number entered is112117.7212.12. 13.2914.160 cm2 15. A car travels 940 kilometers, and B car travels 3 10 kilometers. 16. (See the figure below) 17. (See below)

1. Solve the original formula =

=

= 1÷

=

2. After changing the solution, A studies by himself 1 hour more than B every day, which is 60 minutes.

B Self-study is five days, that is, B now self-study every day: 60 ÷ (6- 1) = 12 (minutes).

The original time for self-study is: 12+30 = 42 (minutes).

3. According to the measurement, the pig's body is surrounded by a circle with a diameter of 42 mm, and each "leg" and a "tail" is a semicircle with a diameter of 6 mm; The pig's head has an outer diameter of 34 mm and an inner diameter of 30 mm. The pig's nose has an outer diameter of14 mm. The unshaded part of the nose consists of two semicircles with a diameter of 5 mm and a rectangle with a height of 5 mm and a width of 3 mm. The nose consists of two semicircles with a diameter of 2 mm.: The "pig eye" consists of two semicircles with a diameter of 5 mm; The "pig mouth" consists of a semicircle with a diameter of 7 mm, so the required area is

≈ 1093 (mm2)

4. The solution is because Wolf △ Wolf = Wolf, the original formula = Sheep △ (Wolf ☆ Sheep) ☆ Sheep △ Wolf,

No matter what the previous result is, the last step of sheep △ wolf or lang △ wolf is always equal to wolf, so the original formula = wolf.

5. Solving the problem shows that each child's parents are of the same blood type, so the parents are all O-type, the child is definitely O-type, the parents are both A-type, and the child is definitely A-type (the case that the child is O-type has been ruled out, and the parents of the 0-type child have been identified as O-type). Parents are AB type and children are B type, that is, children wear red, yellow and blue coats and parents wear blue, yellow and red hats respectively.

6. By moving the white ball and the black ball for the first time and adding 20g to the left plate, the problem of balance is solved, that is, the weight of four black balls is equal to the weight of two white balls plus 20g, and the weight of the right plate is added 50g for the second time, that is, the weight of four white balls is equal to the weight of two black balls plus 50g, that is, the weight of two white balls is equal to 1 black ball plus 20g, so the four black balls are balanced. So the weight of two white balls is 15+25 = 40g, and the weight of 1 white ball is 20g.

7. The solution is that the amount of water injected into the pool when the inlet valve is opened for 30 minutes is equal to 1 the difference between the displacement of the drain valve for 30 minutes and the amount of water filled in the pool; At the same time, it is also equal to the difference between the displacement of two drainage valves for 30 minutes and the water volume of three full pools. Therefore, the displacement of 1 drain valve for 30 minutes is equal to the water volume of two full ponds. In other words, 1 drain valve can drain the water in the pool every minute. Three drain valves can drain the water in the pool every minute. Therefore, when the water inlet valve is closed, it only takes 5 minutes to completely empty the pool water.

A: It will take five minutes.

8. Solution 37 = 3+5+29

=2+5+7+23=3+ 1 1+23

=2+3+ 13+ 19=5+ 13+ 19

=7+ 1 1+ 19=2+5+ 1 1+ 19

=7+ 13+ 17=2+5+ 13+ 17

= 27+ 1 1+ 17

*** 10 different demolition methods, of which 3× 5× 29 = 435 is the smallest.

9. Because the uphill road from A to B is the downhill road from B to A; The downhill from a to b is certain. When it is assumed that the uphill road from B to A is the road from B to C, it is obvious that the distance from A to C is twice as long as that from A to B, exactly half of which is uphill and the other half is downhill. What is the bus time from A to C?

9+7.5 = 16.5 (hours)

Because it takes 1/20 hours per kilometer to go uphill and 1/35 hours per kilometer to go downhill,

So the distance from a to b is equal to 2 10 (km),

If the journey from A to B is uphill, it only takes 20× 9 = 180 (km) in 9 hours. Less than 2 10- 180 = 30 (km)

Downhill is 35-20 = 15 (kilometers) more than uphill, and it takes 30 ÷ 15 = 2 (hours) to walk 30 kilometers more.

So from A to B, it takes 2 hours to go downhill, 9-2 = 7 (hours) and 20× 7 = 140 (kilometers) to go uphill.

Answer: The length of the road between Party A and Party B is 265,438+00 kilometers. From A to B, you need to take an uphill road of 140 km.

Note that this problem can naturally be solved by solving equations. According to the meaning of the question, the uphill road from A to B is X kilometers, and the downhill road is Y kilometers.

So (x+y) (+) = 16.5,

Therefore, x+y = 2 10. Substitute y = 2 10-x into the formula (1) to get x+-x = 9.

That is x+6 = 9 or x = 1, so x = 140.

10. The number in the middle of the solution is 19.95 ÷ 3 = 6.65, so the first number in the second column is 19.95-6.65-8.80 = 4.50.

So? = 19.95-4.33-4.50= 1 1. 12

1 1. Solution If the cylinder can be completely immersed in water, the product of the water depth and the bottom area of the container should be equal to the sum of the volume of the original water and the volume of the cylinder in water, so the water depth is

= 17.72 (cm)

It is greater than the height of the cylinder, so it can be seen that the cylinder can be completely immersed in water, so the required water depth is 17.72 cm.

12. Scheme 1: After part of the liquid in cups 1 and 3 is poured into cup 2, the sugar in cup 1 is 50g, the sugar in cup 2 is 50g, the salt is 25g and the salt in cup 3 is 75g.

Step 2: Pour the No.2 liquid into the 1 cup, where the sugar content is 50+50× = (g) and the salt content is 25× = (g). No.2 cup contains 50× grams of sugar, 25× grams of salt, and No.3 cup contains 75 grams of salt.

Step 3: After the liquid in the No.2 cup is poured into the No.3 cup, the 1 cup contains sugar grams and salt grams; Cup 2 contains 5 o ×××× grams of sugar. The salt content is 25×××× grams; The sugar content of No.3 cup is 5o×××× = (g), and the salt content is 75+25×××× = (g).

So the ratio of salt content to sugar content is 1, 2, 3 cups, followed by 1: 9, 1: 2, 76: 5.

13. Solution When the sum of two numbers is constant, the closer the two numbers are (that is, the smaller the difference), the greater the product, so

8.03× 1.22